OFFSET
1,1
COMMENTS
Even numbers with 2 distinct prime factors where the odd factor is prime.
A proper subset of A098202. E.g., 210 is not here, but it is there. Also differs from A100367: 36, 100, 108, 196, etc. are missing here. Different also from A036348 because 90 and 180 are not here.
Composite numbers k having the property that the number of divisors of 2k equals the number of divisors of k + 2. All primes satisfy this property. - Gary Detlefs, Jan 23 2019
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
FORMULA
Numbers of the form 2^k*p where k > 0, p is an odd prime.
a(n) = 2*A038550(n). - Amiram Eldar, Dec 21 2020
MAPLE
N:= 1000: # to get all terms <= N
P:= select(isprime, [seq(i, i=3..N/2, 2)]):
S:= {seq(seq(2^i*p, i=1..ilog2(N/p)), p=P)}:
sort(convert(S, list)); # Robert Israel, Jul 09 2017
with(numtheory): for n from 1 to 224 do if tau(2*n)=tau(n)+2 and not isprime(n) then print(n) fi od # Gary Detlefs, Jan 22 2019
MATHEMATICA
<<NumberTheory`NumberTheoryFunctions` p2[x_] :=Part[PrimeFactorList[x], 2]; lf[x_] :=Length[FactorInteger[x]]; ta={{0}}; Do[If[Equal[lf[n], 2]&&EvenQ[n]&&IntegerQ[Log[2, n/p2[n]]], ta=Append[ta, n]; Print[n]], {n, 1, 256}]; ta=Delete[ta, 1]
dpf2Q[n_]:=Module[{f=FactorInteger[n]}, Length[f]==2&&f[[1, 1]]==2&&f[[-1, 2]]==1]; Select[Range[2, 250, 2], dpf2Q] (* Harvey P. Dale, Sep 03 2016 *)
PROG
(Haskell)
import Data.Set (singleton, deleteFindMin, insert)
a100368 n = a100368_list !! (n-1)
a100368_list = f (singleton 6) (tail a065091_list) where
f s ps'@(p:ps) | mod m 4 > 0 = m : f (insert (2*p) $ insert (2*m) s') ps
| otherwise = m : f (insert (2*m) s') ps'
where (m, s') = deleteFindMin s
-- Reinhard Zumkeller, Sep 19 2011
(PARI) is(n)=n%2==0 && isprime(n>>valuation(n, 2)) \\ Charles R Greathouse IV, Jul 09 2017
(PARI) list(lim)=my(v=List()); for(k=1, logint(lim\3, 2), forprime(p=3, lim>>k, listput(v, p<<k))); Set(v) \\ Charles R Greathouse IV, Jul 09 2017
(GAP) a:=Filtered([1..224], n->Tau(2*n)=Tau(n)+2 and not IsPrime(n));; Print(a); # Muniru A Asiru, Jan 22 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Labos Elemer, Nov 22 2004
EXTENSIONS
Name edited by Charles R Greathouse IV, Jul 09 2017
STATUS
approved