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

1,2

Links

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

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A000010, A018804.

Sequence in context: A160736 A118030 A187208 * A351623 A256409 A256403

Adjacent sequences: A349722 A349723 A349724 * A349726 A349727 A349728

Keyword

nonn

Author

Ctibor O. Zizka, Nov 27 2021

Status

approved