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

1,2

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

Formula

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

Prog

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

Crossrefs

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

Sequence in context: A329112 A347886 A023389 * A221636 A162018 A055741

Adjacent sequences: A248960 A248961 A248962 * A248964 A248965 A248966

Keyword

nonn

Author

M. F. Hasler, Oct 18 2014

Status

approved