A347880 Numbers k such that A342926(k) is a multiple of 3.

4, 5, 8, 14, 16, 20, 23, 25, 26, 30, 38, 41, 49, 51, 59, 62, 64, 66, 74, 77, 80, 86, 90, 92, 96, 102, 108, 113, 120, 122, 124, 127, 131, 134, 138, 143, 146, 149, 153, 158, 159, 164, 165, 167, 169, 174, 194, 196, 198, 200, 203, 204, 206, 209, 210, 213, 217, 218, 223, 236, 239, 243, 246, 254, 255, 257, 264, 267, 270

Offset: 1

Author

Antti Karttunen, Sep 18 2021

Keywords

• nonn

Crossrefs

Positions of zeros in A347883.

Cf. A000203, A003415, A342926.

Cf. A005820, A342923 (subsequences).

Cf. also A347872.

Programs

Mathematica

ad[1] = 0; ad[n_] := n * Total@(Last[#]/First[#]& /@ FactorInteger[n]); Select[Range[270], Divisible[ad[DivisorSigma[1, #]] - #, 3] &] (* Amiram Eldar, Sep 18 2021 *)

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A342926(n) = (A003415(sigma(n))-n);
isA347880(n) = !(A342926(n)%3);