A257048 - OEIS

%I #10 Apr 22 2015 11:19:17

%S 9,15,16,25,27,35,42,49,72,95,119,121,140,143,154,168,169,200,209,220,

%T 240,256,264,287,288,289,297,315,319,323,342,343,361,364,377,378,442,

%U 483,490,520,525,527,529,540,559,585,588,616,620,624,625,648,693,702,729

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

%H Paolo P. Lava, <a href="/A257048/b257048.txt">Table of n, a(n) for n = 1..1000</a>

%e 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 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 with(numtheory); P:=proc(q) local a,n;

%p for n from 1 to q do a:=ifactors(n)[2];

%p if type(phi(n)/add(a[k][1]*a[k][2],k=1..nops(a)),integer)

%p then print(n); fi; od; end: P(10^9);

%t Rest@ Select[Range@ 729, Mod[EulerPhi@ #, Total@ Flatten[Table[#1, {#2}] & @@@ FactorInteger@ #]] == 0 &] (* _Michael De Vlieger_, Apr 15 2015 *)

%Y Cf. A000010, A161917.

%K nonn,easy

%O 1,1

%A _Paolo P. Lava_, Apr 15 2015