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

Author

M. F. Hasler, Jul 15 2011

Keywords

• nonn

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

Programs

Mathematica

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

PARI

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

Formula

A193071 = A005408 \ A193070.