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A030009 Euler transform of primes. 9
1, 2, 6, 15, 37, 85, 192, 414, 879, 1816, 3694, 7362, 14480, 28037, 53644, 101379, 189587, 350874, 643431, 1169388, 2108045, 3770430, 6694894, 11804968, 20679720, 35999794, 62298755, 107198541, 183462856, 312357002, 529173060, 892216829, 1497454396, 2502190992 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

N. J. A. Sloane, Transforms

FORMULA

G.f.: Product_{n>=1} (1-x^n)^(-prime(n)).

MAPLE

with(numtheory):

a:= proc(n) option remember; `if`(n=0, 1, add(add(

      d*ithprime(d), d=divisors(j))*a(n-j), j=1..n)/n)

    end:

seq(a(n), n=0..40);  #  Alois P. Heinz, Sep 06 2008

MATHEMATICA

a[n_] := a[n] = If[n == 0, 1, Sum[Sum[d*Prime[d], {d, Divisors[j]}]*a[n-j], {j, 1, n}]/n]; Table[a[n], {n, 0, 40}] (* Jean-Fran├žois Alcover, Apr 16 2014, after Alois P. Heinz *)

PROG

(PARI) a(n)=if(n<0, 0, polcoeff(prod(i=1, n, (1-x^i)^-prime(i), 1+x*O(x^n)), n))

CROSSREFS

Cf. A007441.

Sequence in context: A017923 A238830 A018018 * A061261 A291414 A098790

Adjacent sequences:  A030006 A030007 A030008 * A030010 A030011 A030012

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified January 19 16:49 EST 2019. Contains 319309 sequences. (Running on oeis4.)