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A226566
Numbers n such that Sum_{d|n} sigma(d)^3/d is an integer, where d are the divisors of n.
5
1, 201, 981, 1962, 3663, 7326, 10791, 12753, 15879, 21582, 25506, 30411, 56898, 60822, 135749, 140283, 172161, 212454, 266727, 280566, 334521, 344322, 360027, 395343, 399267, 407247, 507177, 625878, 669042, 720054, 739674, 790686, 798534, 881919, 1014354, 1221741
OFFSET
1,2
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..510 (terms below 10^10)
EXAMPLE
Divisors of 981 are 1, 3, 9, 109, 327, 981.
sigma(1) = 1, sigma(3) = 4, sigma(9) = 13, sigma(109) = 110, sigma(327) = 440, sigma(981) = 1430.
(1^3/1 + 4^3/3 + 13^3/9 + 110^3/109 + 440^3/327 + 1430^3/981) = 3253822.
MAPLE
with(numtheory); ListA226566:=proc(q) local a, b, k, n;
for n from 1 to q do a:=[op(divisors(n))]; b:=add(sigma(a[k])^3/a[k], k=1..nops(a));
if type(b, integer) then print(n); fi; od; end: ListA226566(10^6);
MATHEMATICA
aQ[n_] := IntegerQ[DivisorSum[n, DivisorSigma[1, #]^3/# &]]; Select[Range[10^5], aQ] (* Amiram Eldar, Sep 18 2019 *)
PROG
(PARI) isok(n) = denominator(sumdiv(n, d, sigma(d)^3/d)) == 1; \\ Michel Marcus, Sep 18 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Paolo P. Lava, Jun 11 2013
STATUS
approved