A342009 - OEIS

A342009

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

1, 2, 4, 8, 9, 12, 15, 16, 20, 32, 36, 48, 64, 81, 108, 112, 128, 144, 180, 189, 192, 196, 225, 256, 320, 324, 400, 432, 500, 512, 528, 576, 625, 729, 768, 972, 1024, 1225, 1296, 1300, 1360, 1452, 1728, 2048, 2160, 2304, 2700, 2816, 2916, 3024, 3072, 3375, 3564, 3840, 3888, 3993, 4096, 4800, 5120, 5184, 5292, 5616, 6000

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OFFSET

1,2

COMMENTS

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

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..1001

MATHEMATICA

Select[Range[6000], Mod[If[Abs[#] < 2, 0, # Total[#2/#1 & @@@ FactorInteger[Abs@ #]]], EulerPhi[#]] == 0 &] (* Michael De Vlieger, Mar 11 2021 *)

PROG

(PARI)

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));