A349725 Numbers k >= 1 such that A018804(k) divided by A000010(k) is an integer.

1, 2, 4, 8, 12, 16, 20, 32, 36, 48, 64, 100, 108, 112, 128, 132, 144, 192, 256, 320, 324, 432, 500, 512, 576, 756, 768, 784, 960, 972, 1024, 1296, 1452, 1600, 1728, 1892, 2048, 2052, 2112, 2240, 2304, 2500, 2816, 2880, 2916, 3072, 3888, 4096, 4800, 5120, 5184, 5292, 5488

Offset: 1

Author

Ctibor O. Zizka, Nov 27 2021

Keywords

• nonn

Examples

			A018804(20) = 72, A000010(20) = 8, 72/8 = 9 thus 20 is a term.
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000010, 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;Join[{1,2},Reap[Do[If[Divisible[A018804[k],EulerPhi[k]],Sow[k]],{k,4,upto,4}]][[-1,-1]]] (* Paolo Xausa, Jul 25 2022 *)

PARI

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

Formula

For n >= 3, a(n) mod 4 = 0. - Paolo Xausa, Jul 25 2022