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A319088
a(n) = Sum_{k=1..n} k^2*tau_3(k), where tau_3 is A007425.
1
1, 13, 40, 136, 211, 535, 682, 1322, 1808, 2708, 3071, 5663, 6170, 7934, 9959, 13799, 14666, 20498, 21581, 28781, 32750, 37106, 38693, 55973, 59723, 65807, 73097, 87209, 89732, 114032, 116915, 138419, 148220, 158624, 169649, 216305, 220412, 233408, 247097
OFFSET
1,2
LINKS
Eric Weisstein's World of Mathematics, Stieltjes Constants
FORMULA
a(n) ~ n^3 * (log(n)^2/6 + (gamma - 1/9)*log(n) + gamma^2 - gamma/3 - g1 + 1/27), where gamma is the Euler-Mascheroni constant A001620 and g1 is the first Stieltjes constant A082633.
MATHEMATICA
nmax = 50; Accumulate[Table[k^2*Sum[DivisorSigma[0, d], {d, Divisors[k]}], {k, 1, nmax}]]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Sep 10 2018
STATUS
approved