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A257048 Numbers n for which the sum of their prime factors (with repetition) divides the Euler totient function.

%I A257048 #10 Apr 22 2015 11:19:17
%S A257048 9,15,16,25,27,35,42,49,72,95,119,121,140,143,154,168,169,200,209,220,
%T A257048 240,256,264,287,288,289,297,315,319,323,342,343,361,364,377,378,442,
%U A257048 483,490,520,525,527,529,540,559,585,588,616,620,624,625,648,693,702,729
%N A257048 Numbers n for which the sum of their prime factors (with repetition) divides the Euler totient function.
%H A257048 Paolo P. Lava, <a href="/A257048/b257048.txt">Table of n, a(n) for n = 1..1000</a>
%e A257048 The value of Euler totient function for n = 15 is 8. Prime factors of 15 are 3, 5 and their sum is 3 + 5 = 8. Finally, 8 / 8 = 1.
%e A257048 The value of Euler totient function for n = 140 is 48. Prime factors of 140 are 2, 2, 5, 7 and their sum is 2 + 2 + 5 + 7 = 16. Finally, 48 / 16 = 3.
%p A257048 with(numtheory); P:=proc(q) local a,n;
%p A257048 for n from 1 to q do a:=ifactors(n)[2];
%p A257048 if type(phi(n)/add(a[k][1]*a[k][2],k=1..nops(a)),integer)
%p A257048 then print(n); fi; od; end: P(10^9);
%t A257048 Rest@ Select[Range@ 729, Mod[EulerPhi@ #, Total@ Flatten[Table[#1, {#2}] & @@@ FactorInteger@ #]] == 0 &] (* _Michael De Vlieger_, Apr 15 2015 *)
%Y A257048 Cf. A000010, A161917.
%K A257048 nonn,easy
%O A257048 1,1
%A A257048 _Paolo P. Lava_, Apr 15 2015