cp's OEIS Frontend

A342009 Numbers k such that the arithmetic derivative of k is a multiple of phi(k).

%I A342009 #13 Mar 12 2021 23:10:39
%S A342009 1,2,4,8,9,12,15,16,20,32,36,48,64,81,108,112,128,144,180,189,192,196,
%T A342009 225,256,320,324,400,432,500,512,528,576,625,729,768,972,1024,1225,
%U A342009 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
%N A342009 Numbers k such that the arithmetic derivative of k is a multiple of phi(k).
%C A342009 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).
%H A342009 Antti Karttunen, <a href="/A342009/b342009.txt">Table of n, a(n) for n = 1..1001</a>
%t A342009 Select[Range[6000], Mod[If[Abs[#] < 2, 0, # Total[#2/#1 & @@@ FactorInteger[Abs@ #]]], EulerPhi[#]] == 0 &] (* _Michael De Vlieger_, Mar 11 2021 *)
%o A342009 (PARI)
%o A342009 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A342009 isA342009(n) = !(A003415(n)%eulerphi(n));
%Y A342009 Cf. A000010, A003415, A166374 (subsequence), A173557, A342001, A342008.
%Y A342009 Positions of ones in A342415.
%K A342009 nonn
%O A342009 1,2
%A A342009 _Antti Karttunen_, Mar 11 2021