OFFSET
1,2
COMMENTS
Row sums of triangle A329323. - Omar E. Pol, Nov 21 2019
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = Sum_{k*l*m = n} k*l*m, for positive integers k, l, m. This equals one sixth of the same sum over all integers. - Ralf Stephan, May 06 2005
Dirichlet g.f.: zeta^3(x-1).
Multiplicative with a(p^e) = p^e * binomial(e+2, 2). - Mitch Harris, Jun 27 2005
Sum_{k=1..n} a(k) ~ (2*log(n)^2 + (12*gamma - 2)*log(n) + 12*gamma^2 - 6*gamma - 12*sg1 + 1) * n^2 / 8, where gamma is the Euler-Mascheroni constant A001620 and sg1 is the first Stieltjes constant (see A082633). - Vaclav Kotesovec, Sep 11 2019
G.f.: Sum_{k>=1} k*tau(k)*x^k / (1 - x^k)^2, where tau = A000005. - Ilya Gutkovskiy, Sep 22 2020
MATHEMATICA
Table[n*Sum[DivisorSigma[0, d], {d, Divisors[n]}], {n, 1, 100}] (* Vaclav Kotesovec, Aug 31 2018 *)
f[p_, e_] := (e+1)*(e+2)*p^e/2; a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* Amiram Eldar, Sep 29 2020 *)
CROSSREFS
KEYWORD
nonn,mult,easy
AUTHOR
STATUS
approved