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A070222 Numbers n such that the sum of prime divisors of n divides the sum of divisors of n. 3
15, 20, 24, 35, 42, 54, 66, 72, 95, 98, 100, 104, 108, 110, 114, 119, 120, 126, 132, 135, 140, 143, 160, 168, 189, 195, 207, 209, 216, 220, 224, 258, 264, 270, 276, 287, 290, 294, 319, 322, 323, 351, 360, 363, 375, 377, 378, 384, 392, 432, 440, 456, 459, 464 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..54.

EXAMPLE

The sum of divisors of 132 is sigma(132)=336; prime divisors of 132 are 2,3,11 and (336)/(2+3+11)=336/16=21 hence 132 is in the sequence.

MAPLE

with(numtheory): op(select(n->frac(sigma(n)/add(a, a=select(isprime, divisors(n))))=0, [$2..464])); # Paolo P. Lava, Aug 28 2018

MATHEMATICA

Select[Range[2, 464], IntegerQ[DivisorSigma[1, #]/Total[First/@FactorInteger[#]]] &] (* Jayanta Basu, May 16 2013 *)

PROG

(PARI) for(n=2, 700, if(sigma(n)%sumdiv(n, d, isprime(d)*d)==0, print1(n, ", ")))

CROSSREFS

Sequence in context: A322710 A316743 A014603 * A143321 A066860 A120159

Adjacent sequences:  A070219 A070220 A070221 * A070223 A070224 A070225

KEYWORD

easy,nonn

AUTHOR

Benoit Cloitre, May 07 2002

STATUS

approved

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Last modified July 5 16:07 EDT 2020. Contains 335473 sequences. (Running on oeis4.)