A226566 - OEIS

%I #13 Sep 18 2019 13:46:59

%S 1,201,981,1962,3663,7326,10791,12753,15879,21582,25506,30411,56898,

%T 60822,135749,140283,172161,212454,266727,280566,334521,344322,360027,

%U 395343,399267,407247,507177,625878,669042,720054,739674,790686,798534,881919,1014354,1221741

%N Numbers n such that Sum_{d|n} sigma(d)^3/d is an integer, where d are the divisors of n.

%H Amiram Eldar, <a href="/A226566/b226566.txt">Table of n, a(n) for n = 1..510</a> (terms below 10^10)

%e Divisors of 981 are 1, 3, 9, 109, 327, 981.

%e sigma(1) = 1, sigma(3) = 4, sigma(9) = 13, sigma(109) = 110, sigma(327) = 440, sigma(981) = 1430.

%e (1^3/1 + 4^3/3 + 13^3/9 + 110^3/109 + 440^3/327 + 1430^3/981) = 3253822.

%p with(numtheory); ListA226566:=proc(q) local a,b,k,n;

%p for n from 1 to q do a:=[op(divisors(n))]; b:=add(sigma(a[k])^3/a[k],k=1..nops(a));

%p if type(b,integer) then print(n); fi; od; end: ListA226566(10^6);

%t aQ[n_] := IntegerQ[DivisorSum[n, DivisorSigma[1, #]^3/# &]]; Select[Range[10^5], aQ] (* _Amiram Eldar_, Sep 18 2019 *)

%o (PARI) isok(n) = denominator(sumdiv(n, d, sigma(d)^3/d)) == 1; \\ _Michel Marcus_, Sep 18 2019

%Y Cf. A068978, A068986, A226563, A226564, A226565

%K nonn

%O 1,2

%A _Paolo P. Lava_, Jun 11 2013