A267895 Numbers whose number of odd divisors is prime.

3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 17, 18, 19, 20, 22, 23, 24, 25, 26, 28, 29, 31, 34, 36, 37, 38, 40, 41, 43, 44, 46, 47, 48, 49, 50, 52, 53, 56, 58, 59, 61, 62, 67, 68, 71, 72, 73, 74, 76, 79, 80, 81, 82, 83, 86, 88, 89, 92, 94, 96, 97, 98, 100, 101, 103, 104, 106, 107, 109

Offset

1,1

Comments

All odd primes are in the sequence.

Links

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

Example

The divisors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. The odd divisors of 36 are 1, 3, 9. There are 3 odd divisors of 36 and 3 is prime, so 36 is in the sequence.

Mathematica

Select[Range[100], PrimeQ[DivisorSigma[0, #/2^IntegerExponent[#, 2]]] &] (* Amiram Eldar, Dec 03 2020 *)

Prog

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

Crossrefs

Complement of A267894.

Cf. A000040, A001227, A028982, A028983, A038550, A065091, A072502, A266531, A267696, A267697.

Sequence in context: A363690 A052294 A336101 * A216189 A191916 A254614

Adjacent sequences: A267892 A267893 A267894 * A267896 A267897 A267898

Keyword

nonn

Author

Omar E. Pol, Apr 04 2016

Status

approved