A297842 a(n) = Sum_{d|n} max(d, n/d)^3.

1, 16, 54, 136, 250, 486, 686, 1152, 1485, 2250, 2662, 4016, 4394, 6174, 7000, 9280, 9826, 13554, 13718, 18250, 19208, 23958, 24334, 32560, 31375, 39546, 40824, 50078, 48778, 63182, 59582, 74752, 74536, 88434, 86436, 110106, 101306, 123462, 123032, 147024

Offset: 1

Author

Seiichi Manyama, Jan 07 2018

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Sum_{d|n} max(d, n/d)^k: A117003 (k=1), A297841 (k=2), this sequence (k=3), A297843 (k=4), A297844 (k=5).

Cf. A001158, A013662, A297793.

Programs

Mathematica

f[n_] := Block[{d = Divisors@ n}, Plus @@ (Max[#, n/#]^3 & /@ d)]; Array[f, 40] (* Robert G. Wilson v, Jan 07 2018 *)

PARI

{a(n) = sumdiv(n, d, max(d, n/d)^3)}

Formula

a(n) + A297793(n) = 2*A001158(n).

Sum_{k=1..n} a(k) ~ (zeta(4)/2) * n^4. - Amiram Eldar, Jan 12 2025