A347885 Odd numbers k such that sigma(k^2) has an odd number of prime factors when counted with multiplicity.

3, 5, 17, 21, 27, 33, 35, 37, 39, 41, 45, 49, 55, 57, 59, 61, 65, 69, 71, 75, 87, 89, 93, 95, 101, 107, 109, 115, 119, 125, 129, 131, 137, 139, 141, 145, 149, 151, 153, 155, 159, 167, 169, 173, 181, 187, 189, 193, 201, 215, 219, 221, 229, 231, 235, 237, 249, 255, 259, 265, 269, 273, 283, 287, 289, 291, 293, 297, 307

Offset: 1

Author

Antti Karttunen, Sep 19 2021

Keywords

• nonn

Comments

Equally, odd numbers k such that A003415(sigma(k^2)) is odd, i.e., k^2 is in A347877. See A235991.

A square root of any hypothetical odd square x present in A005820 (triperfect numbers) would be a member of this sequence, because bigomega(x) would be even, and bigomega(3*x) would be odd. See also A347887.

Crossrefs

Cf. A000203, A001222, A003415, A235991, A347870, A347877, A347882, A347886 (complement among A005408), A347887 (subsequence).

Programs

Mathematica

Select[Range[1, 300, 2], OddQ[PrimeOmega[DivisorSigma[1, #^2]]] &] (* Amiram Eldar, Sep 19 2021 *)

PARI

isA347885(n) = ((n%2)&&(bigomega(sigma(n^2))%2));