A342008 Numbers k such that Euler totient phi(k) is a multiple of the arithmetic derivative of k.

2, 3, 5, 7, 9, 11, 13, 15, 17, 19, 23, 25, 29, 31, 35, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 73, 79, 83, 89, 95, 97, 101, 103, 107, 109, 113, 119, 121, 127, 131, 137, 139, 143, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 209, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281

Offset: 1

Author

Antti Karttunen, Mar 12 2021

Keywords

• nonn

Comments

Numbers k for which A000010(k) is a multiple of A003415(k), or equally, k for which A173557(k) is a multiple of A342001(k).

Crossrefs

Cf. A000010, A003415, A173557, A342001, A342009.

Subsequences: A000040, A166374, A342418 (composite terms).

Positions of ones in A342414.

Programs

Mathematica

Select[Range[2, 281], Mod[EulerPhi[#], If[# < 2, 0, # Total[#2/#1 & @@@ FactorInteger[#]] ] &@ Abs[#]] == 0 &] (* Michael De Vlieger, Mar 12 2021 *)

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
isA342008(n) = ((n>1)&&!(eulerphi(n)%A003415(n)));
for(n=2,2^8,if(isA342008(n),print1(n,", ")));