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A030009
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Euler transform of primes.
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10
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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
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: Product_{n>=1} (1-x^n)^(-prime(n)).
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MAPLE
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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:
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MATHEMATICA
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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-François Alcover, Apr 16 2014, after Alois P. Heinz *)
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PROG
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(PARI) a(n)=if(n<0, 0, polcoeff(prod(i=1, n, (1-x^i)^-prime(i), 1+x*O(x^n)), n))
(SageMath) # uses[EulerTransform from A166861]
b = EulerTransform(lambda n: nth_prime(n))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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