A161917 Numbers n for which the sum of their prime factors (with repetition) divides the sum of their divisors.

12, 15, 35, 42, 60, 63, 66, 68, 84, 90, 95, 110, 114, 119, 140, 143, 152, 168, 189, 195, 204, 209, 216, 234, 245, 258, 264, 270, 280, 287, 290, 294, 297, 319, 322, 323, 352, 368, 377, 380, 384, 396, 470, 476, 480, 506, 510, 527, 531, 544, 552, 558, 559, 572

Offset: 1

Author

Paolo P. Lava and Giorgio Balzarotti, Jun 23 2009

Keywords

• easy
• nonn

Examples

			n=12: Sum_divisors (1,2,3,4,6,12) = 28; Sum_prime_factors (2,2,3) =7 -> 28/7 = 4. n=319: Sum_divisors (1,11,29,319) = 360; Sum_prime_factors (11,29) =40 -> 360/40 = 9.
		

Links

• Carl R. White, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A161918

Programs

Maple

with(numtheory); P:=proc(q) local a,n;
for n from 2 to q do if not isprime(n) then a:=ifactors(n)[2];
if type(sigma(n)/add(a[k][1]*a[k][2],k=1..nops(a)),integer) then print(n);
fi; fi; od; end: P(10^4);

Mathematica

Select[Range[2,600],Divisible[DivisorSigma[1,#],Total[ Times@@@ FactorInteger[#]]]&] (* Harvey P. Dale, Dec 09 2010 *)

Formula

{n: A001414(n) | A000203(n)}. - R. J. Mathar, Jun 26 2009

Extensions

Offset corrected by R. J. Mathar, Jun 26 2009