A390663 The sum of the divisors of the smallest cube divisible by n.

1, 15, 40, 15, 156, 600, 400, 15, 40, 2340, 1464, 600, 2380, 6000, 6240, 127, 5220, 600, 7240, 2340, 16000, 21960, 12720, 600, 156, 35700, 40, 6000, 25260, 93600, 30784, 127, 58560, 78300, 62400, 600, 52060, 108600, 95200, 2340, 70644, 240000, 81400, 21960, 6240

Offset

1,2

Comments

First differs from A369720 and A369758 at n = 16.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = A000203(A053149(n)).

a(n) >= A000203(n) with equality if and only if n is a cube (A000578).

Multiplicative with a(p^e) = (p^(e + 1 + ((3-e) mod 3)) - 1)/(p-1).

Sum_{k=1..n} a(k) ~ c * n^4 / 4, where c = zeta(4) * zeta(9) * Product_{p prime} (1 - 1/p^4 - 1/p^9 + 1/p^10) = 1.00092987505793961871... .

Mathematica

f[p_, e_] := (p^(e + 1 + Mod[3 - e, 3]) - 1)/(p - 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]

Prog

(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, (f[i, 1]^(f[i, 2] + 1 + (3-f[i, 2])%3) - 1) / (f[i, 1] - 1)); }

Crossrefs

Cf. A000203, A000578, A053149, A365346, A365489, A369717, A369720, A369758, A390664.

Cf. A013662, A013667.

Sequence in context: A062222 A369720 A369758 * A325659 A223432 A044092

Adjacent sequences: A390660 A390661 A390662 * A390664 A390665 A390666

Keyword

nonn,mult,easy

Author

Amiram Eldar, Nov 14 2025

Status

approved