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Search: id:A030009
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| A030009 |
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Euler transform of primes. |
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+0
5
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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
(list; graph; listen)
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OFFSET
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0,2
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LINKS
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N. J. A. Sloane, Transforms
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FORMULA
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G.f.: Product_{n=1..inf} (1-x^n)^-ithprime(n).
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MAPLE
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with (numtheory): a:= proc(n) option remember; local d, j; if n=0 then 1 else (add (d*ithprime(d), d=divisors(n)) +add (add (d*ithprime(d), d=divisors(j)) *a(n-j), j=1..n-1))/n fi end: seq (a(n), n=0..30); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 06 2008]
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PROGRAM
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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))
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CROSSREFS
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Cf. A007441.
Adjacent sequences: A030006 A030007 A030008 this_sequence A030010 A030011 A030012
Sequence in context: A084798 A017923 A018018 this_sequence A061261 A098790 A018019
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KEYWORD
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nonn
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AUTHOR
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njas
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