OFFSET
1,2
COMMENTS
Inverse Moebius transform of A000219.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..10000
N. J. A. Sloane, Transforms
Eric Weisstein's World of Mathematics, Plane Partition
MAPLE
b:= proc(n) option remember; `if`(n=0, 1, add(
b(n-j)*numtheory[sigma][2](j), j=1..n)/n)
end:
a:= n-> add(b(d), d=numtheory[divisors](n)):
seq(a(n), n=1..40); # Alois P. Heinz, Jun 21 2018
MATHEMATICA
nmax = 37; Rest[CoefficientList[Series[Sum[-1 + Product[1/(1 - x^(k j))^j, {j, 1, nmax}], {k, 1, nmax}], {x, 0, nmax}], x]]
b[n_] := b[n] = SeriesCoefficient[Product[1/(1 - x^k)^k , {k, 1, n}], {x, 0, n}]; a[n_] := a[n] = SeriesCoefficient[Sum[b[k] x^k/(1 - x^k), {k, 1, n}], {x, 0, n}]; Table[a[n], {n, 37}]
b[0] = 1; b[n_] := b[n] = Sum[b[n - j] DivisorSigma[2, j], {j, n}]/n; a[n_] := a[n] = Sum[b[d], {d, Divisors[n]}]; Table[a[n], {n, 37}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jun 20 2018
STATUS
approved