OFFSET
1,2
COMMENTS
Inverse Moebius transform of A026007.
LINKS
N. J. A. Sloane, Transforms
MAPLE
with(numtheory):
b:= proc(n) option remember;
add((-1)^(n/d+1)*d^2, d=divisors(n))
end:
g:= proc(n) option remember;
`if`(n=0, 1, add(b(k)*g(n-k), k=1..n)/n)
end:
a:= n-> add(g(d), d=divisors(n)):
seq(a(n), n=1..40); # Alois P. Heinz, Jun 21 2018
MATHEMATICA
nmax = 40; Rest[CoefficientList[Series[Sum[-1 + Product[(1 + x^(k j))^j, {j, 1, nmax}], {k, 1, nmax}], {x, 0, nmax}], x]]
b[n_] := b[n] = SeriesCoefficient[Product[(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, 40}]
b[0] = 1; b[n_] := b[n] = Sum[Sum[(-1)^(j/d + 1) d^2, {d, Divisors[j]}] b[n - j], {j, n}]/n; a[n_] := a[n] = Sum[b[d], {d, Divisors[n]}]; Table[a[n], {n, 40}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jun 20 2018
STATUS
approved