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A226565 Numbers k such that Sum_{d|k} sigma(d)^3 is a multiple of k. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 27 12:24 EST 2023. Contains 359840 sequences. (Running on oeis4.)