|
%I #12 Jul 10 2018 19:23:52
%S 18,36,72,96,140,144,234,288,336,468,486,490,576,825,864,924,936,972,
%T 980,1008,1120,1152,1248,1872,1944,1960,2300,2304,2310,2352,2592,2673,
%U 2772,2964,3024,3040,3234,3332,3500,3610,3744,3840,3888,3920,4235,4329
%N 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.
%H Robert Israel, <a href="/A070224/b070224.txt">Table of n, a(n) for n = 1..10000</a>
%e 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.
%p filter:= proc(n) (numtheory:-sigma[2](n)/add(p^2, p=numtheory:-factorset(n)))::integer end proc:
%p select(filter, [$2..10000]); # _Robert Israel_, Jul 10 2018
%t Select[Range[2,5000],Divisible[DivisorSigma[2,#],Total[FactorInteger[#][[All, 1]]^2]]&] (* _Harvey P. Dale_, Apr 02 2018 *)
%o (PARI) for(n=2,10000,if(sumdiv(n,d,d^2)%sumdiv(n,d,isprime(d)*d^2)==0,print1(n,",")))
%K easy,nonn
%O 1,1
%A _Benoit Cloitre_, May 07 2002
|
