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A070224 Numbers k such that the sum of p^2, where p are the prime divisors of k, divides the sum of d^2, where d are the divisors of k. 1
18, 36, 72, 96, 140, 144, 234, 288, 336, 468, 486, 490, 576, 825, 864, 924, 936, 972, 980, 1008, 1120, 1152, 1248, 1872, 1944, 1960, 2300, 2304, 2310, 2352, 2592, 2673, 2772, 2964, 3024, 3040, 3234, 3332, 3500, 3610, 3744, 3840, 3888, 3920, 4235, 4329 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

The sum of square divisors of 2352 is sigma_2(2352)=8357910; prime divisors of 2352 are 2,3,7 and (8357910)/(2^2+3^2+7^2)=8357910/62=134805 hence 2352 is in the sequence.

MAPLE

filter:= proc(n) (numtheory:-sigma[2](n)/add(p^2, p=numtheory:-factorset(n)))::integer end proc:

select(filter, [$2..10000]); # Robert Israel, Jul 10 2018

MATHEMATICA

Select[Range[2, 5000], Divisible[DivisorSigma[2, #], Total[FactorInteger[#][[All, 1]]^2]]&] (* Harvey P. Dale, Apr 02 2018 *)

PROG

(PARI) for(n=2, 10000, if(sumdiv(n, d, d^2)%sumdiv(n, d, isprime(d)*d^2)==0, print1(n, ", ")))

CROSSREFS

Sequence in context: A154575 A097926 A087967 * A083211 A156903 A204824

Adjacent sequences:  A070221 A070222 A070223 * A070225 A070226 A070227

KEYWORD

easy,nonn

AUTHOR

Benoit Cloitre, May 07 2002

STATUS

approved

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Last modified May 26 19:44 EDT 2019. Contains 323597 sequences. (Running on oeis4.)