OFFSET
1,2
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..100000
Vaclav Kotesovec, Graph - The asymptotic ratio (1000000 terms)
FORMULA
a(n) = Sum_{k=1..n} A034718(k).
a(n) ~ n^2 * (log(n)^2 + (6*g-1)*log(n) + 6*g^2 - 3*g - 6*g1 + 1/2) / 4, where g is the Euler-Mascheroni constant A001620 and g1 is the first Stieltjes constant A082633. - Vaclav Kotesovec, Sep 09 2018
MATHEMATICA
Accumulate[Table[n*Sum[DivisorSigma[0, d], {d, Divisors[n]}], {n, 1, 100}]]
(* Asymptotics: *) n^2 * (Log[n]^2 + (6*EulerGamma - 1)*Log[n] + 6*EulerGamma^2 - 3*EulerGamma - 6*StieltjesGamma[1] + 1/2) / 4 (* Vaclav Kotesovec, Sep 09 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Sep 02 2018
STATUS
approved