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
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..2000
- N. J. A. Sloane, Transforms
Programs
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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}]
Formula
G.f.: 1/(1 - Sum_{k>=2} A001221(k)*x^k).
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