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A190402 Number n for which phi(n) = phi(n'), where phi is the Euler totient function and n' the arithmetic derivative of n.

%I A190402 #16 Aug 08 2015 02:26:41
%S A190402 2,4,8,14,20,27,45,52,75,148,195,244,292,364,628,729,772,1108,1196,
%T A190402 1215,1252,1406,1552,1588,1684,1701,1828,2164,2452,2644,2692,2924,
%U A190402 2932,3028,3125,3508,3825,3982,3988,4372,4462,4612,4804,4852,4948,5284,5524
%N A190402 Number n for which phi(n) = phi(n'), where phi is the Euler totient function and n' the arithmetic derivative of n.
%H A190402 Nathaniel Johnston, <a href="/A190402/b190402.txt">Table of n, a(n) for n = 1..2500</a>
%p A190402 with(numtheory);
%p A190402 P:=proc(i)
%p A190402 local f,n,p,pfs;
%p A190402 for n from 1 to i do
%p A190402     pfs:=ifactors(n)[2];
%p A190402     f:=n*add(op(2,p)/op(1,p),p=pfs);
%p A190402     if phi(n)=phi(f) then print(n); fi;
%p A190402 od;
%p A190402 end:
%p A190402 P(1000);
%t A190402 d[0] = d[1] = 0; d[n_] := n*Total[f = FactorInteger[n]; f[[All, 2]]/f[[All, 1]] ]; Reap[For[n = 1, n < 6000, n++, If[EulerPhi[n] == EulerPhi[d[n]], Sow[n]]]][[2, 1]] (* _Jean-François Alcover_, Apr 22 2015 *)
%Y A190402 Cf. A000010, A003415, A166374, A190403.
%K A190402 nonn
%O A190402 1,1
%A A190402 _Paolo P. Lava_, May 10 2011