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

1,1

Links

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

Example

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.

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 *)

Crossrefs

Cf. A000010, A161917.

Sequence in context: A136410 A324879 A066942 * A363896 A061838 A037002

Adjacent sequences: A257045 A257046 A257047 * A257049 A257050 A257051

Keyword

nonn,easy

Author

Paolo P. Lava, Apr 15 2015

Status

approved