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Search: a010553 -id:a010553
Displaying 1-10 of 28 results found. page 1 2 3
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A335831 Numbers k with a record value of tau(tau(k)) (A010553), where tau(k) is the number of divisors of k (A000005). +20
2
1, 2, 6, 12, 60, 360, 1260, 2520, 5040, 55440, 277200, 720720, 3603600, 61261200, 129729600, 908107200, 2205403200, 15437822400, 293318625600, 3226504881600, 6746328388800, 74209612276800, 195643523275200, 1855240306920000, 2152078756027200, 27977023828353600 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
First differs from A189394 at n=15.
The corresponding record values are 1, 2, 3, 4, 6, 8, 9, 10, 12, 16, 18, 20, 24, 30, ... (see the link for more values).
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..73
Yvonne Buttkewitz, Christian Elsholtz, Kevin Ford and Jan-Christoph Schlage-Puchta, A problem of Ramanujan, Erdős, and Kátai on the iterated divisor function, International Mathematics Research Notices, Vol. 2012, No. 17 (2012), pp. 4051-4061, preprint, arXiv:1108.1815 [math.NT], 2011.
Amiram Eldar, Table of n, a(n), A010553(a(n)) for n = 1..73
Christian Elsholtz, Marc Technau and Niclas Technau, The maximal order of iterated multiplicative functions, Mathematika, Vol. 65, No. 4 (2019), pp. 990-1009, preprint, arXiv:1709.04799 [math.NT], 2017 and 2019.
FORMULA
tau(tau(a(n))) ~ c * sqrt(log(a(n)))/log(log(a(n))), where c is a constant (Buttkewitz et al., 2012).
MATHEMATICA
f[n_] := DivisorSigma[0, DivisorSigma[0, n]]; fm = 0; s = {}; Do[f1 = f[n]; If[f1 > fm, fm = f1; AppendTo[s, n]], {n, 1, 10^5}]; s
CROSSREFS
Subsequence of A025487.
Cf. A000005, A005179, A010553, A189394, A193987.
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jun 25 2020
STATUS
approved
A083399 Number of divisors of n that are not divisors of other divisors of n. +10
19
1, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 3, 2, 3, 3, 2, 2, 3, 2, 3, 3, 3, 2, 3, 2, 3, 2, 3, 2, 4, 2, 2, 3, 3, 3, 3, 2, 3, 3, 3, 2, 4, 2, 3, 3, 3, 2, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 2, 4, 2, 3, 3, 2, 3, 4, 2, 3, 3, 4, 2, 3, 2, 3, 3, 3, 3, 4, 2, 3, 2, 3, 2, 4, 3, 3, 3, 3, 2, 4, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 2, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
a(n)<=tau(n); a(n)=tau(n) iff n is prime or n=1 (A008578, A000040); a(n)=tau(n)-1 iff n is semiprime (A001358).
Number of noncomposite divisors of n, (cf. A008578). - Jaroslav Krizek, Nov 25 2009
From Wilf A. Wilson, Jul 21 2017: (Start)
a(n) is the number of maximal subsemigroups of the annular Jones monoid of degree n.
a(n) is the number of maximal subsemigroups of the monoid of orientation-preserving mappings on a set with n elements.
a(n) + 1 is the number of maximal subsemigroups of the monoid of orientation-preserving partial mappings on a set with n elements.
(End)
This is the restricted growth sequence transform of A001221 (and thus also of A007875, A034444, A082476, A292586 and many other sequences). This follows from the formula a(n) = 1+A001221(n), and from the fact that for any n, A001221(n) <= 1+A001221(k) for all k = 1..(n-1). A067003 gives the ordinal transform of A001221. See also A292582, A292583, A292585. - Antti Karttunen, Sep 25 2017
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
James East, Jitender Kumar, James D. Mitchell, and Wilf A. Wilson, Maximal subsemigroups of finite transformation and partition monoids, arXiv:1706.04967 [math.GR], 2017. [Wilf A. Wilson, Jul 21 2017]
FORMULA
a(n) = omega(n) + 1, where omega = A001221.
a(n) = tau(n) - A055212(n) = A000005(n)-A055212(n).
a(n) = A000005(n) - A033273(n) + 1. - Jaroslav Krizek, Nov 25 2009
a(n) = A010553(A007947(n)) = A000005(A000005(A007947(n))) = tau_2(tau_2(rad(n))). - Enrique Pérez Herrero, Jun 25 2010
G.f.: x/(1 - x) + Sum_{k>=1} x^prime(k)/(1 - x^prime(k)). - Ilya Gutkovskiy, Mar 21 2017
EXAMPLE
{1,2,3,4,6,8,12,24} are the divisors of n=24: 1, 2, 3, 4 and 6 divide not only 24, but also 8 or 12, therefore a(24)=3.
{1,2,3,4,6,8,12,24} are the divisors of n=24: 1, 2 and 3 are noncomposites, therefore a(24)=3. - Jaroslav Krizek, Nov 25 2009
MAPLE
A083399 := proc(n)
1+nops(numtheory[factorset](n)) ;
end proc:
seq(A083399(n), n=1..100) ; # R. J. Mathar, Sep 26 2017
MATHEMATICA
A083399[n_Integer]:=1+PrimeNu[n]; (* Enrique Pérez Herrero, Jun 25 2010 *)
Rest@ CoefficientList[ Series[(1/(1 - x)) + Sum[1/(1 - x^Prime[j]), {j, 200}], {x, 0, 111}], x] (* Robert G. Wilson v, Aug 16 2011 *)
PROG
(Magma) [(#(PrimeDivisors(n)))+1: n in [1..100]]; // Vincenzo Librandi, Feb 15 2015
(PARI) a(n)=#factor(n)~+1 \\ Charles R Greathouse IV, Sep 14 2015
(Haskell)
a083399 = (+ 1) . a001221 -- Reinhard Zumkeller, Sep 14 2015
CROSSREFS
Cf. A000005, A001221, A067003, A055212.
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Jun 12 2003
STATUS
approved
A212171 Prime signature of n (nonincreasing version): row n of table lists positive exponents in canonical prime factorization of n, in nonincreasing order. +10
17
1, 1, 2, 1, 1, 1, 1, 3, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 4, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 4, 1, 2, 2, 1, 1, 1, 2, 1, 1, 3, 1, 1, 1, 3, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,3
COMMENTS
Length of row n equals A001221(n).
The multiset of positive exponents in n's prime factorization completely determines a(n) for a host of OEIS sequences, including several "core" sequences. Of those not cross-referenced here or in A212172, many can be found by searching the database for A025487.
(Note: Differing opinions may exist about whether the prime signature of n should be defined as this multiset itself, or as a symbol or collection of symbols that identify or "signify" this multiset. The definition of this sequence is designed to be compatible with either view, as are the original comments. When n >= 2, the customary ways to signify the multiset of exponents in n's prime factorization are to list the constituent exponents in either nonincreasing or nondecreasing order; this table gives the nonincreasing version.)
Table lists exponents in the order in which they appear in the prime factorization of a member of A025487. This ordering is common in database comments (e.g., A008966).
Each possible multiset of an integer's positive prime factorization exponents corresponds to a unique partition that contains the same elements (cf. A000041). This includes the multiset of 1's positive exponents, { } (the empty multiset), which corresponds to the partition of 0.
Differs from A124010 from a(23) on, corresponding to the factorization of 18 = 2^1*3^2 which is here listed as row 18 = [2, 1], but as [1, 2] (in the order of the prime factors) in A124010 and also in A118914 which lists the prime signatures in nondecreasing order (so that row 12 = 2^2*3^1 is also [1, 2]). - M. F. Hasler, Apr 08 2022
LINKS
Jason Kimberley, Table of i, a(i) for i = 2..24301 (n = 2..10000)
FORMULA
Row n of A118914, reversed.
Row n of A124010 for n > 1, with exponents sorted in nonincreasing order. Equivalently, row A046523(n) of A124010 for n > 1.
EXAMPLE
First rows of table read:
1;
1;
2;
1;
1,1;
1;
3;
2;
1,1;
1;
2,1;
...
The multiset of positive exponents in the prime factorization of 6 = 2*3 is {1,1} (1s are often left implicit as exponents). The prime signature of 6 is therefore {1,1}.
12 = 2^2*3 has positive exponents 2 and 1 in its prime factorization, as does 18 = 2*3^2. Rows 12 and 18 of the table both read {2,1}.
PROG
(Magma) &cat[Reverse(Sort([pe[2]:pe in Factorisation(n)])):n in[1..76]]; // Jason Kimberley, Jun 13 2012
(PARI) apply( {A212171_row(n)=vecsort(factor(n)[, 2]~, , 4)}, [1..40])\\ M. F. Hasler, Apr 19 2022
CROSSREFS
Cf. A025487, A001221 (row lengths), A001222 (row sums). A118914 gives the nondecreasing version. A124010 lists exponents in n's prime factorization in natural order, with A124010(1) = 0.
A212172 cross-references over 20 sequences that depend solely on n's prime exponents >= 2, including the "core" sequence A000688. Other sequences determined by the exponents in the prime factorization of n include:
Multiplicative: A000005, A007425, A008683, A008836, A034444, A037445, A181819.
Additive: A001221, A001222, A056169.
Other: A001055, A008480, A010553, A038548, A050320, A051707, A071625, A074206, A076078, A085082, A088873.
A highly incomplete selection of sequences, each definable by the set of prime signatures possessed by its members: A000040, A000290, A000578, A000583, A000961, A001248, A001358, A001597, A001694, A002808, A004709, A005117, A006881, A013929, A030059, A030229, A052486.
KEYWORD
nonn,easy,tabf
AUTHOR
Matthew Vandermast, Jun 03 2012
STATUS
approved
A036450 a(n) = d(d(d(n))), the 3rd iterate of the number-of-divisors function with an initial value of n. +10
15
1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 3, 2, 3, 2, 3, 3, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 2, 2, 4, 2, 2, 3, 2, 2, 3, 2, 3, 2, 3, 2, 4, 2, 2, 3, 3, 2, 3, 2, 3, 2, 2, 2, 4, 2, 2, 2, 3, 2, 4, 2, 3, 2, 2, 2, 4, 2, 3, 3, 2, 2, 3, 2, 3, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
The iterated d function rapidly converges to the fixed point 2.
From N. J. A. Sloane, Jun 02 2014: (Start)
The fourth iterate begins as follows:
1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, ... . (End)
REFERENCES
S. Ramanujan, Collected Papers, Ed. G. H. Hardy et al., Cambridge 1927; Chelsea, NY, 1962, p. 128. - N. J. A. Sloane, Jun 02 2014
LINKS
Enrique Pérez Herrero, Table of n, a(n) for n = 1..2000
R. Bellman and H. N. Shapiro, On a problem in additive number theory, Annals Math., 49 (1948), 333-340.
EXAMPLE
n = 5040, d(5040) = 60, d(d(5040)) = d(60) = 12 and a(5040) = d(12) = 6.
MATHEMATICA
f[n_]:=Length[Divisors[n]]; Table[Nest[f, n, 3], {n, 6!}] (* Vladimir Joseph Stephan Orlovsky, Mar 10 2010 *)
PROG
(PARI) a(n)=numdiv(numdiv(numdiv(n))) \\ Charles R Greathouse IV, Nov 16 2022
(Python)
from sympy import divisor_count
def A036450(n): return divisor_count(divisor_count(divisor_count(n))) # Chai Wah Wu, Nov 17 2022
CROSSREFS
Cf. A000005, A010553, A036452, A036453.
KEYWORD
nonn
AUTHOR
Labos Elemer
STATUS
approved
A036452 a(n) = d(d(d(d(n)))), the 4th iterate of number-of-divisors function with initial value of n. +10
11
1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
The iterated d function rapidly converges to fixed point 2. For k=4, the first n for which a(n)>2 is 60.
LINKS
Enrique Pérez Herrero, Table of n, a(n) for n = 1..2000
FORMULA
a(n) = d(d(d(d(n)))).
EXAMPLE
E.g., n=96 and its successive iterates are 12,6,4,3 and 2. The 4th term is a(96)=3.
MATHEMATICA
f[n_]:=DivisorSigma[0, n]; Table[Nest[f, n, 4], {n, 100}] (* Vladimir Joseph Stephan Orlovsky, Mar 10 2010 *)
PROG
(PARI) a(n)=my(d=numdiv); d(d(d(d(n)))) \\ Charles R Greathouse IV, Apr 07 2012
CROSSREFS
Cf. A000005, A010553, A036450, A036453.
KEYWORD
nonn
AUTHOR
Labos Elemer
STATUS
approved
A036453 a(n) = d(d(d(d(d(n))))), the 5th iterate of the number-of-divisors function d = A000005, with initial value n. +10
9
1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
The iterated d function rapidly converges to fixed point 2. In the 5th iterated d-sequence, the first term different from the fixed point 2 appears at n = 5040. The 6th and further iterated sequences have very long initial segment of 2's. In the 6th one the first non-stationary term is a(293318625600) = 3. In such sequences any large value occurs infinite many times and constructible.
Differs from A007395 for n = 1, 5040, 7920, 8400, 9360, 10080, 10800, etc. - R. J. Mathar, Oct 20 2008
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
EXAMPLE
E.g., n = 96 and its successive iterates are 12, 6, 4, 3 and 2. The 5th term is a(96) = 2 is stationary (fixed).
MATHEMATICA
Table[Nest[DivisorSigma[0, #]&, n, 5], {n, 110}] (* Harvey P. Dale, Jun 18 2021 *)
PROG
(PARI) a(n)=my(d=numdiv); d(d(d(d(d(n))))) \\ Charles R Greathouse IV, Apr 07 2012
CROSSREFS
Cf. A000005, A010553, A036450, A036452.
KEYWORD
nonn
AUTHOR
Labos Elemer
EXTENSIONS
Previous Mathematica program replaced by Harvey P. Dale, Jun 18 2021
STATUS
approved
A036454 Prime powers with special exponents: q^(p-1) where p > 2 and q are prime numbers. +10
7
4, 9, 16, 25, 49, 64, 81, 121, 169, 289, 361, 529, 625, 729, 841, 961, 1024, 1369, 1681, 1849, 2209, 2401, 2809, 3481, 3721, 4096, 4489, 5041, 5329, 6241, 6889, 7921, 9409, 10201, 10609, 11449, 11881, 12769, 14641, 15625, 16129, 17161, 18769, 19321 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Composite numbers with a prime number of divisors.
LINKS
T. D. Noe, Table of n, a(n) for n = 1..1000
FORMULA
d(d(a(n))) = 2, where d(x) = tau(x) = sigma_0(x) is the number of divisors of x.
a(n) = (n log n)^2 + 2n^2 log n log log n + O(n^2 log n). - Charles R Greathouse IV, Apr 26 2012
(1 - A010051(a(n))) * A010055(a(n)) * A010051(A100995(a(n))+1) = 1. - Reinhard Zumkeller, Jun 05 2013
A036459(a(n)) = 2. - Ivan Neretin, Jan 25 2016
a(n) = A283262(n)^2. - Amiram Eldar, Jul 04 2022
Sum_{n>=1} 1/a(n) = Sum_{k>=2} P(prime(k)-1) = 0.54756961912815344341..., where P is the prime zeta function. - Amiram Eldar, Jul 10 2022
EXAMPLE
From powers of 2: 4,16,64,1024,4096,65536 are in the sequence since exponent+1 is also prime. The same powers of any prime base are also included.
MAPLE
N:= 10^5:
P1:= select(isprime, [2, seq(2*i+1, i=1..floor((sqrt(N)-1)/2))]):
P2:= select(`<=`, P1, 1+ilog2(N))[2..-1]:
S:= {seq(seq(p^(q-1), q = select(`<=`, P2, 1+floor(log[p](N)))), p=P1)}:
sort(convert(S, list)); # Robert Israel, May 18 2015
MATHEMATICA
specialPrimePowerQ[n_] := With[{f = FactorInteger[n]}, Length[f] == 1 && PrimeQ[f[[1, 1]]] && f[[1, 2]] > 1 && PrimeQ[f[[1, 2]] + 1]]; Select[Range[20000], specialPrimePowerQ] (* Jean-François Alcover, Jul 02 2013 *)
Select[Range[20000], ! PrimeQ[#] && PrimeQ[DivisorSigma[0, #]] &] (* Carlos Eduardo Olivieri, May 18 2015 *)
PROG
(PARI) for(n=1, 34000, if(isprime(n), n++, x=numdiv(n); if(isprime(x), print(n))))
(PARI) list(lim)=my(v=List(), t); lim=lim\1+.5; forprime(p=3, log(lim)\log(2) +1, t=p-1; forprime(q=2, lim^(1/t), listput(v, q^t))); vecsort(Vec(v))
\\ Charles R Greathouse IV, Apr 26 2012
(Haskell)
a009087 n = a009087_list !! (n-1)
a009087_list = filter ((== 1) . a010051 . (+ 1) . a100995) a000961_list
-- Reinhard Zumkeller, Jun 05 2013
(Magma) [n: n in [1..20000] | not IsPrime(n) and IsPrime(DivisorSigma(0, n))]; // Vincenzo Librandi, May 19 2015
CROSSREFS
Intersection of A002808 and A009087.
Cf. A000005, A010051, A010553, A010055, A100995, A036450, A036452, A036459, A283262.
KEYWORD
nonn,easy,nice
AUTHOR
Labos Elemer
STATUS
approved
A141113 Positive integers k such that d(d(k)) divides k, where d(k) is the number of divisors of k. +10
4
1, 2, 4, 6, 12, 15, 16, 20, 21, 24, 27, 28, 32, 33, 36, 39, 40, 44, 48, 51, 52, 56, 57, 60, 64, 68, 69, 72, 76, 80, 84, 87, 88, 90, 92, 93, 96, 104, 108, 111, 112, 116, 120, 123, 124, 126, 128, 129, 132, 136, 141, 144, 148, 150, 152, 156, 159, 164, 172, 176, 177, 180 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
Jinyuan Wang, Table of n, a(n) for n = 1..10000
EXAMPLE
28 has 6 divisors and 6 has 4 divisors. 4 divides 28, so 28 is in the sequence.
MAPLE
with(numtheory): a:=proc(n) if `mod`(n, tau(tau(n))) = 0 then n else end if end proc: seq(a(n), n=1..200); # Emeric Deutsch, Jun 05 2008
MATHEMATICA
Select[Range[200], Divisible[#, DivisorSigma[0, DivisorSigma[0, #]]]&] (* Harvey P. Dale, Feb 05 2012 *)
PROG
(PARI) is(k) = k%numdiv(numdiv(k)) == 0; \\ Jinyuan Wang, Feb 19 2019
CROSSREFS
Cf. A000005 (tau), A010553, A141114, A141115.
KEYWORD
nonn
AUTHOR
Leroy Quet, Jun 04 2008
EXTENSIONS
More terms from Emeric Deutsch, Jun 05 2008
STATUS
approved
A141114 Positive integers k where d(d(k)) is coprime to k, where d(k) is the number of divisors of k. +10
3
1, 3, 5, 7, 8, 9, 10, 11, 13, 14, 17, 19, 22, 23, 25, 26, 29, 31, 34, 35, 37, 38, 41, 43, 45, 46, 47, 49, 53, 55, 58, 59, 61, 62, 63, 65, 67, 71, 73, 74, 75, 77, 79, 81, 82, 83, 85, 86, 89, 91, 94, 95, 97, 99, 100, 101, 103, 105, 106, 107, 109, 113, 115, 117, 118, 119, 121 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Includes all primes, squares of odd primes, and squarefree semiprimes coprime to 3. - Robert Israel, Dec 16 2019
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
26 has 4 divisors and 4 has 3 divisors. 3 is coprime to 26, so 26 is in the sequence.
MAPLE
filter:= proc(n) uses numtheory;
igcd(tau(tau(n)), n) = 1
end proc:
select(filter, [$1..200]); # Robert Israel, Dec 16 2019
MATHEMATICA
Select[Range[200], GCD[DivisorSigma[0, DivisorSigma[0, # ]], # ] == 1 &] (* Stefan Steinerberger, Jun 05 2008 *)
PROG
(Magma) [k:k in [1..130]|Gcd(k, #Divisors(#Divisors(k))) eq 1]; // Marius A. Burtea, Dec 16 2019
(PARI) is(n) = gcd(numdiv(numdiv(n)), n)==1 \\ Felix Fröhlich, Dec 16 2019
CROSSREFS
Cf. A010553, A141113, A141115.
KEYWORD
nonn
AUTHOR
Leroy Quet, Jun 04 2008
EXTENSIONS
More terms from Stefan Steinerberger, Jun 05 2008
STATUS
approved
A141115 Those positive integers k where both d(d(k)) is not coprime to k and d(d(k)) does not divide k, where d(k) is the number of divisors of k. +10
3
18, 30, 42, 50, 54, 66, 70, 78, 98, 102, 110, 114, 130, 138, 140, 154, 160, 162, 170, 174, 182, 186, 190, 200, 220, 222, 224, 230, 238, 242, 246, 250, 258, 260, 266, 282, 286, 290, 308, 310, 315, 318, 322, 338, 340, 350, 352, 354, 364, 366, 370, 374, 380, 392 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
50 has 6 divisors and 6 has 4 divisors. 4 is not coprime to 50 and 4 does not divide 50. So 50 is in the sequence.
MATHEMATICA
Select[Range[400], GCD[DivisorSigma[0, DivisorSigma[0, # ]], # ] > 1 && Mod[ #, DivisorSigma[0, DivisorSigma[0, # ]]] > 0 &] (* Stefan Steinerberger, Jun 05 2008 *)
CROSSREFS
Cf. A010553, A141113, A141114.
KEYWORD
nonn
AUTHOR
Leroy Quet, Jun 04 2008
EXTENSIONS
More terms from Stefan Steinerberger, Jun 05 2008
STATUS
approved
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Last modified August 18 17:33 EDT 2024. Contains 375269 sequences. (Running on oeis4.)