A226566 Numbers n such that Sum_{d|n} sigma(d)^3/d is an integer, where d are the divisors of n.

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

Cf. A068978, A068986, A226563, A226564, A226565

Sequence in context: A157956 A202771 A183350 * A061697 A371109 A371057

Adjacent sequences: A226563 A226564 A226565 * A226567 A226568 A226569

Keyword

nonn

Author

Paolo P. Lava, Jun 11 2013

Status

approved