OFFSET
1,2
FORMULA
a(n) = Sum_{k=1..n} k * Sum_{d|k} d^(d-1).
G.f.: (1/(1-x)) * Sum_{k>=1} (k * x)^k/(1 - x^k)^2.
MATHEMATICA
a[n_] := Sum[k^k * Binomial[Floor[n/k] + 1, 2], {k, 1, n}]; Array[a, 18] (* Amiram Eldar, Jul 28 2022*)
PROG
(PARI) a(n) = sum(k=1, n, k^k*binomial(n\k+1, 2));
(PARI) a(n) = sum(k=1, n, k*sumdiv(k, d, d^(d-1)));
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, (k*x)^k/(1-x^k)^2)/(1-x))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jul 27 2022
STATUS
approved