A193071 Odd numbers N for which sigma(N^2) is not prime.

1, 7, 9, 11, 13, 15, 19, 21, 23, 25, 29, 31, 33, 35, 37, 39, 43, 45, 47, 51, 53, 55, 57, 61, 63, 65, 67, 69, 73, 75, 77, 79, 81, 83, 85, 87, 91, 93, 95, 97, 99, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 127, 129, 133, 135, 137, 139, 141, 143, 145, 147

Offset

1,2

Comments

The function sigma(n) (=A000203(n)) takes odd values when n is a square or twice a square. Thus, odd numbers n for which sigma(n) is prime (cf. A023194) must be odd squares. This sequence gives the odd numbers whose square yields a composite sum of divisors (or 1).

This is the complement of A193070 in the odd numbers A005408.

Links

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

Formula

A193071 = A005408 \ A193070.

Mathematica

Select[Range[1, 151, 2], !PrimeQ[DivisorSigma[1, #^2]]&] (* Harvey P. Dale, Dec 13 2012 *)

Prog

(PARI) forstep(N=1, 1e7, 2, !isprime(sigma(N^2)) && print1(N", "))

Crossrefs

Sequence in context: A066669 A059808 A020742 * A329112 A347886 A023389

Adjacent sequences: A193068 A193069 A193070 * A193072 A193073 A193074

Keyword

nonn

Author

M. F. Hasler, Jul 15 2011

Status

approved