A248963 Prime powers p^m for which sigma(p^2m) is not prime.

1, 7, 9, 11, 13, 16, 19, 23, 25, 29, 31, 32, 37, 43, 47, 53, 61, 67, 73, 79, 81, 83, 97, 103, 107, 109, 113, 121, 127, 128, 137, 139, 149, 151, 157, 163, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 243, 251, 257, 263, 269, 271, 277, 281, 283, 307, 311, 313, 317, 331

Offset: 1

Author

M. F. Hasler, Oct 18 2014

Keywords

• nonn

Comments

sigma(x) cannot be prime unless x is a square of a prime power, x = p^2m, cf. A055638 and A023194. This sequence lists the complement: prime powers whose square does not have a prime sum of divisors.

Although generally 1 is not considered a prime power, it seemed logical for various good reasons to include the initial term a(1)=1.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000961, A055638, A023194, A023195, A062700.

Programs

PARI

for(n=1,999,isprimepower(n)||next;isprime(sigma(n^2))||print1((n)","))

Formula

A248963 = A000961 \ A055638, i.e., the complement of A055638 in A000961.