A267894 Numbers whose number of odd divisors is nonprime.

1, 2, 4, 8, 15, 16, 21, 27, 30, 32, 33, 35, 39, 42, 45, 51, 54, 55, 57, 60, 63, 64, 65, 66, 69, 70, 75, 77, 78, 84, 85, 87, 90, 91, 93, 95, 99, 102, 105, 108, 110, 111, 114, 115, 117, 119, 120, 123, 125, 126, 128, 129, 130, 132, 133, 135, 138, 140, 141, 143, 145, 147, 150

Offset: 1

Author

Omar E. Pol, Apr 04 2016

Keywords

• nonn

Examples

			The divisors of 42 are 1, 2, 3, 6, 7, 14, 21, 42. The odd divisors of 42 are 1, 3, 7, 21. There are 4 odd divisors of 42 and 4 is a nonprime number, so 42 is in the sequence.
		

Links

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

Crossrefs

Cf. A000079, A001227, A018252, A028982, A028983, A131651, A230577, A266531, A267891, A267892, A267893, A267895.

Programs

Mathematica

Select[Range[150], !PrimeQ[DivisorSigma[0, #/2^IntegerExponent[#, 2]]] &] (* Amiram Eldar, Dec 03 2020 *)

PARI

isok(n) = ! isprime(sumdiv(n, d, (d%2))); \\ Michel Marcus, Apr 04 2016