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A300671 Expansion of 1/(1 - Sum_{k>=1} x^prime(k)/(1 - x^prime(k))). 2

%I

%S 1,0,1,1,2,3,6,8,15,23,40,63,108,172,290,471,782,1280,2119,3474,5741,

%T 9432,15557,25590,42180,69413,114371,188276,310136,510637,841045,

%U 1384883,2280831,3755862,6185457,10185941,16774695,27624215,45492412,74916559,123374127,203172520,334587577

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

%C Invert transform of A001221.

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

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

%t nmax = 42; CoefficientList[Series[1/(1 - Sum[x^Prime[k]/(1 - x^Prime[k]), {k, 1, nmax}]), {x, 0, nmax}], x]

%t nmax = 42; CoefficientList[Series[1/(1 - Sum[PrimeNu[k] x^k, {k, 2, nmax}]), {x, 0, nmax}], x]

%t a[0] = 1; a[n_] := a[n] = Sum[PrimeNu[k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 42}]

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

%K nonn

%O 0,5

%A _Ilya Gutkovskiy_, Mar 11 2018

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Last modified April 3 01:31 EDT 2020. Contains 333195 sequences. (Running on oeis4.)