OFFSET
1,2
COMMENTS
In general, for m>=0, Sum_{k=1..n} k^m * tau(k) ~ n^(m+1) * ((log(n) + 2*gamma)/(m+1) - 1/(m+1)^2), where gamma is the Euler-Mascheroni constant A001620.
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..10000
Vaclav Kotesovec, Graph - The asymptotic ratio (1000000 terms)
FORMULA
a(n) ~ n^4 * (log(n) + 2*gamma - 1/4)/4, where gamma is the Euler-Mascheroni constant A001620.
a(n) = Sum_{k=1..n} (k^3 / 4) * floor(n/k)^2 * floor(1 + n/k)^2. - Daniel Suteu, Nov 07 2018
MATHEMATICA
Accumulate[Table[k^3*DivisorSigma[0, k], {k, 1, 50}]]
PROG
(PARI) a(n) = sum(k=1, n, k^3*numdiv(k)); \\ Michel Marcus, Oct 23 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Oct 23 2018
STATUS
approved