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.

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

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: A344199 A097926 A087967 * A083211 A156903 A204824

Adjacent sequences: A070221 A070222 A070223 * A070225 A070226 A070227

Keyword

easy,nonn

Author

Benoit Cloitre, May 07 2002

Status

approved