OFFSET
1,2
COMMENTS
In general, for m>=0, Sum_{k=1..n} k^m / floor(n/k) ~ n^(m+1) * (-1 + Sum_{j=2..m+2} zeta(j) / (m+1)).
FORMULA
a(n) ~ c * n^3 * n!, where c = Sum_{j>=1} (1 + 3*j*(j+1)) / (3*j^4*(j+1)^3) = (zeta(4) + zeta(3) + zeta(2))/3 - 1 = Pi^2/18 + Pi^4/270 + zeta(3)/3 - 1.
MATHEMATICA
Table[n!*Sum[k^2/Floor[n/k], {k, 1, n}], {n, 1, 25}]
Table[n!*Sum[(Floor[n/j]*(1 + Floor[n/j])*(1 + 2*Floor[n/j]) - Floor[n/(1 + j)]*(1 + Floor[n/(1 + j)])*(1 + 2*Floor[n/(1 + j)]))/6/j, {j, 1, n}], {n, 1, 25}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Jun 23 2021
STATUS
approved