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A300671 Expansion of 1/(1 - Sum_{k>=1} x^prime(k)/(1 - x^prime(k))). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Invert transform of A001221.

LINKS

Table of n, a(n) for n=0..42.

N. J. A. Sloane, Transforms

FORMULA

G.f.: 1/(1 - Sum_{k>=2} A001221(k)*x^k).

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

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Last modified February 21 16:21 EST 2020. Contains 332100 sequences. (Running on oeis4.)