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A161917 Numbers n for which the sum of their prime factors (with repetition) divides the sum of their divisors. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

FORMULA

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

EXAMPLE

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.

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 *)

CROSSREFS

Cf. A161918

Sequence in context: A179148 A194234 A296796 * A065150 A277082 A087098

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

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Last modified May 21 03:22 EDT 2018. Contains 304349 sequences. (Running on oeis4.)