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

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]));
isA342009(n) = !(A003415(n)%eulerphi(n));

Crossrefs

Cf. A000010, A003415, A166374 (subsequence), A173557, A342001, A342008.

Positions of ones in A342415.

Sequence in context: A326673 A297126 A044814 * A304451 A098374 A182852

Adjacent sequences: A342006 A342007 A342008 * A342010 A342011 A342012

Keyword

nonn

Author

Antti Karttunen, Mar 11 2021

Status

approved