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

9, 15, 16, 25, 27, 35, 42, 49, 72, 95, 119, 121, 140, 143, 154, 168, 169, 200, 209, 220, 240, 256, 264, 287, 288, 289, 297, 315, 319, 323, 342, 343, 361, 364, 377, 378, 442, 483, 490, 520, 525, 527, 529, 540, 559, 585, 588, 616, 620, 624, 625, 648, 693, 702, 729

Offset: 1

Author

Paolo P. Lava, Apr 15 2015

Keywords

• nonn
• easy

Examples

			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.
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.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000010, A161917.

Programs

Maple

with(numtheory); P:=proc(q) local a,n;
for n from 1 to q do a:=ifactors(n)[2];
if type(phi(n)/add(a[k][1]*a[k][2],k=1..nops(a)),integer)
then print(n); fi; od; end: P(10^9);

Mathematica

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