OFFSET
1,2
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
FORMULA
G.f.: Sum_{k>=1} k * x^k/(1 - x^k)^4 = Sum_{k>=1} binomial(k+2,3) * x^k/(1 - x^k)^2.
MAPLE
f:= n -> n/6*add((d+1)*(d+2), d=numtheory:-divisors(n)):
map(f, [$1..100]); # Robert Israel, Apr 26 2021
MATHEMATICA
a[n_] := n * DivisorSum[n, Binomial[# + 2, 3]/# &]; Array[a, 50] (* Amiram Eldar, Apr 25 2021 *)
PROG
(PARI) a(n) = n*sumdiv(n, d, binomial(d+2, 3)/d);
(PARI) my(N=66, x='x+O('x^N)); Vec(sum(k=1, N, binomial(k+2, 3)*x^k/(1-x^k)^2))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 19 2021
STATUS
approved