A349726 Numbers k >= 1 such that A018804(k) divided by A000203(k) is an integer.

1, 2, 40, 44, 220, 252, 752, 980, 2940, 3680, 4508, 10080, 10780, 11016, 12224, 14432, 16072, 17384, 26096, 26216, 36672, 36848, 44064, 45792, 55080, 60588, 61120, 64288, 72160, 80360, 82656, 85536, 88396, 88944, 93568, 95256, 112000, 112572, 120320, 134464, 144752

Offset: 1

Author

Ctibor O. Zizka, Nov 27 2021

Keywords

• nonn

Examples

			k = 40 : A018804(40) = 180, A000203(40) = 90, 180/90 = 2 thus 40 is a term.
		

Crossrefs

Cf. A000203, A018804.

Programs

Mathematica

A018804[n_]:=Apply[Times,Apply[((#1-1)#2/#1+1)#1^#2&,FactorInteger[n],{1}]]; (* After Amiram Eldar in A018804 *)
upto=10^5;Reap[Do[If[IntegerQ[A018804[k]/DivisorSigma[1,k]],Sow[k]],{k,upto}]][[-1,-1]] (* Paolo Xausa, Aug 18 2022 *)

PARI

isok(k) = (sumdiv(k, d, k*eulerphi(d)/d) % sigma(k)) == 0; \\ Michel Marcus, Nov 27 2021

Extensions

a(12)-a(36) from Paolo Xausa, Nov 27 2021

More terms from Amiram Eldar, Nov 27 2021