A226565 Numbers k such that Sum_{d|k} sigma(d)^3 is a multiple of k.

1, 2, 14, 32, 39, 42, 78, 96, 105, 117, 126, 133, 189, 195, 210, 224, 234, 266, 288, 378, 390, 399, 465, 480, 546, 585, 672, 793, 798, 930, 975, 1170, 1197, 1248, 1365, 1470, 1586, 1638, 1862, 1950, 1995, 2016, 2379, 2394, 2646, 2730, 3255, 3360, 3393, 3591

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..5000 (terms 1..100 from Paolo P. Lava)

Example

Divisors of 189 are 1, 3, 7, 9, 21, 27, 63, 189, sigma(1) = 1, sigma(3) = 4, sigma(7) = 8, sigma(9) = 13, sigma(21) = 32, sigma(27) = 40, sigma(63) = 104, sigma(189) = 320. (1^3 + 4^3 + 8^3 + 13^3 + 32^3 + 40^3 + 104^3 + 320^3) / 189 = 179854.

Maple

with(numtheory); ListA226565:=proc(q) local a, b, k, n;
for n from 1 to q do a:=[op(divisors(n))]; b:=add(sigma(a[k])^3/n, k=1..nops(a));
if type(b, integer) then print(n); fi; od; end: ListA226565 (10^6);

Mathematica

Select[Range[4000], Divisible[Total[DivisorSigma[1, #]^3&/@Divisors[#]], #]&] (* Harvey P. Dale, Sep 17 2019 *)
s[n_] := DivisorSum[n, DivisorSigma[1, #]^3 &]; Select[Range[3600], Divisible[s[#], #] &] (* Amiram Eldar, Jul 01 2022 *)

Crossrefs

Cf. A068978, A068986, A226563, A226564, A226566, A344044.

Sequence in context: A335200 A294558 A202638 * A231050 A337338 A322074

Adjacent sequences: A226562 A226563 A226564 * A226566 A226567 A226568

Keyword

nonn

Author

Paolo P. Lava, Jun 11 2013

Status

approved