OFFSET
0,5
COMMENTS
Invert transform of A001222.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..2000
N. J. A. Sloane, Transforms
FORMULA
G.f.: 1/(1 - Sum_{k>=2} A001222(k)*x^k).
MAPLE
a:= proc(n) option remember; `if`(n=0, 1,
add(a(n-i)*numtheory[bigomega](i), i=1..n))
end:
seq(a(n), n=0..42); # Alois P. Heinz, Feb 11 2021
MATHEMATICA
nmax = 41; CoefficientList[Series[1/(1 - Sum[Boole[PrimePowerQ[k]] x^k/(1 - x^k), {k, 1, nmax}]), {x, 0, nmax}], x]
nmax = 41; CoefficientList[Series[1/(1 - Sum[PrimeOmega[k] x^k, {k, 2, nmax}]), {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = Sum[PrimeOmega[k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 41}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Mar 11 2018
STATUS
approved