OFFSET
1,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..10000
FORMULA
MATHEMATICA
Table[Sum[Floor[n/k]^5, {k, 1, n}], {n, 1, 40}]
Accumulate[Table[DivisorSigma[0, k] - 5*DivisorSigma[1, k] + 10*DivisorSigma[2, k] - 10*DivisorSigma[3, k] + 5*DivisorSigma[4, k], {k, 1, 40}]]
PROG
(PARI) a(n) = sum(k=1, n, (n\k)^5); \\ Michel Marcus, Sep 03 2018
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, (k^5-(k-1)^5)*x^k/(1-x^k))/(1-x)) \\ Seiichi Manyama, May 27 2021
(Python)
from math import isqrt
def A318744(n): return -(s:=isqrt(n))**6+sum((q:=n//k)*(k**5-(k-1)**5+q**4) for k in range(1, s+1)) # Chai Wah Wu, Oct 26 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Sep 02 2018
STATUS
approved