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A320895 a(n) = Sum_{k=1..n} k^3 * tau(k), where tau is A000005. 5
1, 17, 71, 263, 513, 1377, 2063, 4111, 6298, 10298, 12960, 23328, 27722, 38698, 52198, 72678, 82504, 117496, 131214, 179214, 216258, 258850, 283184, 393776, 440651, 510955, 589687, 721399, 770177, 986177, 1045759, 1242367, 1386115, 1543331, 1714831, 2134735 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A141959 A347334 A290243 * A288748 A069496 A047978
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Oct 23 2018
STATUS
approved

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Last modified July 24 13:53 EDT 2024. Contains 374584 sequences. (Running on oeis4.)