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

1,1

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.

Links

Table of n, a(n) for n=1..69.

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A020592 A295387 A263258 * A326653 A218624 A152078

Adjacent sequences: A347882 A347883 A347884 * A347886 A347887 A347888

Keyword

nonn

Author

Antti Karttunen, Sep 19 2021

Status

approved