A347877 Numbers k for which A003415(sigma(k)) is odd.

2, 4, 5, 9, 10, 13, 16, 17, 20, 25, 26, 29, 32, 34, 37, 40, 41, 45, 52, 53, 58, 61, 64, 68, 72, 73, 74, 80, 82, 89, 90, 97, 98, 101, 104, 106, 109, 113, 116, 117, 122, 128, 136, 137, 146, 148, 149, 153, 157, 160, 162, 164, 173, 178, 180, 181, 193, 194, 196, 197, 200, 202, 208, 212, 218, 226, 229, 232, 233, 234

Offset: 1

Author

Antti Karttunen, Sep 19 2021

Keywords

• nonn

Comments

Numbers k such that A342925(k) == 1 (mod 2).

Squares present in this sequence are terms of A347885 squared. (There are no even squares present, see A235991 for the explanation).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A000203, A003415, A023194 (subsequence), A235991, A342925, A347872, A347873, A347885, A347878 (complement).

Cf. A347870 (characteristic function), A349909 (its partial sums).

Programs

Mathematica

ad[1] = 0; ad[n_] := n * Total@(Last[#]/First[#]& /@ FactorInteger[n]); Select[Range[234], OddQ[ad[DivisorSigma[1, #]]] &] (* Amiram Eldar, Sep 19 2021 *)

Formula

For all n >= 1, A349909(a(n)) = n. - Antti Karttunen, Feb 23 2022