A300671 Expansion of 1/(1 - Sum_{k>=1} x^prime(k)/(1 - x^prime(k))).

1, 0, 1, 1, 2, 3, 6, 8, 15, 23, 40, 63, 108, 172, 290, 471, 782, 1280, 2119, 3474, 5741, 9432, 15557, 25590, 42180, 69413, 114371, 188276, 310136, 510637, 841045, 1384883, 2280831, 3755862, 6185457, 10185941, 16774695, 27624215, 45492412, 74916559, 123374127, 203172520, 334587577

Offset

0,5

Comments

Invert transform of A001221.

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} A001221(k)*x^k).

Maple

a:= proc(n) option remember; `if`(n=0, 1,
      add(a(n-i)*nops(ifactors(i)[2]), i=1..n))
    end:
seq(a(n), n=0..42);  # Alois P. Heinz, Feb 11 2021

Mathematica

nmax = 42; CoefficientList[Series[1/(1 - Sum[x^Prime[k]/(1 - x^Prime[k]), {k, 1, nmax}]), {x, 0, nmax}], x]
nmax = 42; CoefficientList[Series[1/(1 - Sum[PrimeNu[k] x^k, {k, 2, nmax}]), {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = Sum[PrimeNu[k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 42}]

Crossrefs

Cf. A001221, A013939, A112965, A129921, A180305, A293548, A300672.

Sequence in context: A129374 A209405 A048809 * A268645 A047001 A174021

Adjacent sequences: A300668 A300669 A300670 * A300672 A300673 A300674

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 11 2018

Status

approved