cp's OEIS Frontend

A189057 Numbers n for which phi(n)=sigma(n'), where phi is the Euler totient function, sigma is the sum of divisors and n' the arithmetic derivative of n.

%I A189057 #23 Mar 30 2012 18:53:49
%S A189057 2,57,175,357,381,543,777,903,2379,3027,6807,25823,47047,74333,82621,
%T A189057 136213,153425,163471,194873,230547,257799,259555,265111,269545,
%U A189057 285439,289009,302403,305305,311395,354365,416005,484169,569245,718333,755885,781501,1012505
%N A189057 Numbers n for which phi(n)=sigma(n'), where phi is the Euler totient function, sigma is the sum of divisors and n' the arithmetic derivative of n.
%H A189057 Donovan Johnson, <a href="/A189057/b189057.txt">Table of n, a(n) for n = 1..300</a>
%e A189057 phi(57)=36. 57'=22 and sigma(22)=36
%e A189057 phi(1012505)=725760. 1012505'=310156 and sigma(310156)=725760
%p A189057 with(numtheory);
%p A189057 P:=proc(i)
%p A189057 local f, n, p, pfs;
%p A189057 for n from 1 by 1 to i do
%p A189057     pfs:=ifactors(n)[2];
%p A189057     f:=n*add(op(2, p)/op(1, p), p=pfs);
%p A189057     if phi(n)=sigma(f) then print(n); fi;
%p A189057 od;
%p A189057 end:
%p A189057 P(1000000)
%Y A189057 Cf. A000010, A000203, A003415, A166374, A190402, A190403.
%K A189057 nonn
%O A189057 1,1
%A A189057 _Paolo P. Lava_, May 17 2011