A297844 a(n) = Sum_{d|n} max(d, n/d)^5.

1, 64, 486, 2080, 6250, 16038, 33614, 67584, 118341, 206250, 322102, 515264, 742586, 1109262, 1525000, 2163712, 2839714, 3912786, 4952198, 6606250, 8201816, 10629366, 12872686, 16504000, 19534375, 24505338, 28815912, 35529998, 41022298, 50334302

Offset: 1

Author

Seiichi Manyama, Jan 07 2018

Keywords

• nonn

Comments

If p is a prime, then 2*p^5 belongs to this sequence. Conjecture: The converse is true. - Alexandra Hercilia Pereira Silva, Oct 04 2022

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), A297843 (k=4), this sequence (k=5).

Cf. A001160, A013664, A297795.

Programs

Mathematica

f[n_] := Block[{d = Divisors@ n}, Plus @@ (Max[#, n/#]^5 & /@ d)]; Array[f, 32] (* Robert G. Wilson v, Jan 07 2018 *)

PARI

{a(n) = sumdiv(n, d, max(d, n/d)^5)}

Formula

a(n) + A297795(n) = 2*A001160(n).

Sum_{k=1..n} a(k) ~ (zeta(6)/3) * n^6. - Amiram Eldar, Jan 12 2025