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A342008 Numbers k such that Euler totient phi(k) is a multiple of the arithmetic derivative of k. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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).

LINKS

Table of n, a(n) for n=1..71.

MATHEMATICA

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

PROG

(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, ", ")));

CROSSREFS

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

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

Positions of ones in A342414.

Sequence in context: A005357 A324697 A082664 * A095737 A054022 A185603

Adjacent sequences:  A342005 A342006 A342007 * A342009 A342010 A342011

KEYWORD

nonn

AUTHOR

Antti Karttunen, Mar 12 2021

STATUS

approved

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Last modified October 23 20:31 EDT 2021. Contains 348215 sequences. (Running on oeis4.)