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%I #13 Jul 11 2019 17:48:47
%S 31,32,80,81,112,176,192,244,368,752,859,912,944,1296,1328,1712,1723,
%T 2672,2864,3024,3632,4208,5552,5744,6128,6156,7472,7664,8048,8748,
%U 9008,9392,11504,13424,13808,14192,15728,16304,18992,20412,20528,20912,21104,21872
%N Numbers equal to the arithmetic derivative of their Euler totient function.
%C Solutions of the equation n = (phi(n))’.
%H Amiram Eldar, <a href="/A248815/b248815.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..500 from Paolo P. Lava)
%e Euler totient function of 32 is 16 and the arithmetic derivative of 16 is 32.
%p with(numtheory): P:= proc(q) local a,n,p; for n from 1 to q do
%p a:=phi(n)*add(op(2,p)/op(1,p),p=ifactors(phi(n))[2]);
%p if n=a then print(n); fi; od; end: P(10^9);
%t deriv[n_] := n*Total[#2/#1 & @@@ FactorInteger[n]]; aQ[1] = 1; aQ[n_] := deriv[EulerPhi[n]] == n; Select[Range[25000], aQ] (* _Amiram Eldar_, Jul 11 2019 *)
%Y Cf. A000005, A003415, A166374.
%K nonn
%O 1,1
%A _Paolo P. Lava_, Oct 15 2014