A297843 a(n) = Sum_{d|n} max(d, n/d)^4.

1, 32, 162, 528, 1250, 2754, 4802, 8704, 13203, 21250, 29282, 44576, 57122, 81634, 102500, 139520, 167042, 225666, 260642, 341250, 393764, 497794, 559682, 715808, 781875, 971074, 1076004, 1310946, 1414562, 1743842, 1847042, 2236416, 2401124, 2839714, 3006052

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), A297842 (k=3), this sequence (k=4), A297844 (k=5).

Cf. A001159, A013663, A297794.

Programs

Mathematica

f[n_] := Block[{d = Divisors@ n}, Plus @@ (Max[#, n/#]^4 & /@ d)]; Array[f, 35] (* Robert G. Wilson v, Jan 07 2018 *)

PARI

{a(n) = sumdiv(n, d, max(d, n/d)^4)}

Formula

a(n) + A297794(n) = 2*A001159(n).

Sum_{k=1..n} a(k) ~ (2*zeta(5)/5) * n^5. - Amiram Eldar, Jan 12 2025