A266531 -id:A266531 - cp's OEIS frontend

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

Omar E. Pol, Apr 04 2016

nonn

All odd primes are in the sequence.

			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.

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

Complement of A267894.

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

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

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

A267894 Numbers whose number of odd divisors is nonprime.

Original entry on oeis.org

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

Omar E. Pol, Apr 04 2016

nonn

			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.

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

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

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

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

A347202 Numbers whose number of odd divisors is not equal to 2.

Original entry on oeis.org

1, 2, 4, 8, 9, 15, 16, 18, 21, 25, 27, 30, 32, 33, 35, 36, 39, 42, 45, 49, 50, 51, 54, 55, 57, 60, 63, 64, 65, 66, 69, 70, 72, 75, 77, 78, 81, 84, 85, 87, 90, 91, 93, 95, 98, 99, 100, 102, 105, 108, 110, 111, 114, 115, 117, 119, 120, 121, 123, 125, 126, 128, 129, 130

Offset: 1

Omar E. Pol, Aug 22 2021

nonn

Numbers that are not products of an odd prime and a power of 2.

Numbers k such that the symmetric representation of sigma(k) has a number of subparts not equal to 2.

Robert Israel, Table of n, a(n) for n = 1..10000

Members of A266531 (sorted), except the column 2.

Cf. A001227, A038550 (complement), A237593, A279387 (subparts).

filter:= proc(n) not isprime(n/2^padic:-ordp(n,2)) end proc:
select(filter, [$1..200]); # Robert Israel, May 09 2025

A347202Q[k_] := !PrimeQ[k/2^IntegerExponent[k, 2]];
Select[Range[200], A347202Q] (* Paolo Xausa, May 12 2025 *)

isok(m) = sumdiv(m, d, d%2) != 2; \\ Michel Marcus, Aug 23 2021

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A267895 Numbers whose number of odd divisors is prime.

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A267894 Numbers whose number of odd divisors is nonprime.

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A347202 Numbers whose number of odd divisors is not equal to 2.

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