

A193071


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


2



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
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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

Table of n, a(n) for n=1..62.


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 * A023389 A248963 A221636
Adjacent sequences: A193068 A193069 A193070 * A193072 A193073 A193074


KEYWORD

nonn


AUTHOR

M. F. Hasler, Jul 15 2011


STATUS

approved



