OFFSET
1,1
COMMENTS
sigma(n) is the sum of the divisors of n (A000203).
If sigma(x) is prime, then x=2 or x=p^(2m), an even power of a prime, cf. A023194. This sequence lists the values n = p^m such that sigma(n^2) is prime, i.e., sqrt( A023194 \ {2} ). The corresponding primes sigma(n^2)=A062700(n) are 1+p+...+p^(2m) = (p^(2m+1)-1)/(p-1), and any prime of that form (cf. A023195) corresponds to a term p^m is in this sequence. - M. F. Hasler, Oct 14 2014
This is a subsequence of A000961, see A248963 for its complement therein. - M. F. Hasler, Oct 19 2014
a(n) nearly always has digitsum of the form 1 mod 3. Specifically, 99.8% of the first 33733 entries examined conformed. The first exceptions are 3, 4, 27, 49, 64, 169, 256, 289, 529, 729. The exceptions (examined) appear to be integer powers themselves excepting the initial 3. Similarly, except for the initial 3, all entries of A023195 appear to have digitsum = 1 mod 3. - Bill McEachen, Mar 05 2017
Number of terms < 10^k: 5, 13, 36, 137, 735, 4730, 33732, 253393, ..., . Robert G. Wilson v, Mar 09 2017
Primes in the sequence are A053182. - Thomas Ordowski, Nov 18 2017
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 1..10000 (first 4730 terms from T. D. Noe)
FORMULA
a(n) = sqrt(A023194(n+1)).
MATHEMATICA
Select[Range[2000], PrimeQ[DivisorSigma[1, #^2]] &]
PROG
(PARI) for(n=1, 9999, isprime(sigma(n^2))&&print1(n", ")) \\ M. F. Hasler, Oct 18 2014
(Magma) [n: n in [1..2000] | IsPrime(SumOfDivisors(n^2))]; // Vincenzo Librandi, Oct 18 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Jun 07 2000
EXTENSIONS
Minor edits by M. F. Hasler, Oct 18 2014
STATUS
approved