A161917 Numbers 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

1,1

Links

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

Formula

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

Example

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

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 *)

Prog

(PARI) isok(k) = if(k < 2, 0, my(f = factor(k)); !(sigma(f) % (f[, 1]~ * f[, 2]))); \\ Amiram Eldar, Mar 07 2026

Crossrefs

Cf. A000203, A001414, A161918.

A037074 is a subsequence.

Sequence in context: A194234 A296796 A376430 * A065150 A365850 A277082

Adjacent sequences: A161914 A161915 A161916 * A161918 A161919 A161920

Keyword

easy,nonn

Author

Paolo P. Lava and Giorgio Balzarotti, Jun 23 2009

Extensions

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

Status

approved