OFFSET
0,5
LINKS
N. J. A. Sloane, Transforms
FORMULA
MAPLE
with(numtheory):
a:= proc(n) option remember; `if`(n=0, 1, add(add(d*
(tau(d)-1), d=divisors(j))*a(n-j), j=1..n)/n)
end:
seq(a(n), n=0..50); # Alois P. Heinz, Sep 03 2018
MATHEMATICA
nmax = 48; CoefficientList[Series[Product[1/(1 - x^k)^(DivisorSigma[0, k] - 1), {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 48; CoefficientList[Series[Exp[Sum[DivisorSigma[1, k] x^(2 k)/(k (1 - x^k)), {k, 1, nmax}]], {x, 0, nmax}], x]
a[n_] := a[n] = If[n == 0, 1, Sum[Sum[d (DivisorSigma[0, d] - 1), {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 48}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Sep 03 2018
STATUS
approved