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Search: id:A084993
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| A084993 |
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Total number of parts in all partitions of n into prime parts. |
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+0
3
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| 0, 1, 1, 2, 3, 5, 6, 9, 12, 16, 20, 27, 33, 42, 53, 64, 80, 96, 117, 141, 169, 201, 239, 282, 333, 390, 456, 532, 617, 715, 826, 951, 1094, 1253, 1435, 1636, 1864, 2119, 2404, 2723, 3078, 3473, 3915, 4403, 4947, 5549, 6215, 6952, 7767, 8665, 9656, 10748
(list; graph; listen)
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OFFSET
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1,4
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FORMULA
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G.f.=sum(x^p(j)/(1-x^p(j)),j=1..infinity)/product(1-x^p(j), j=1..infinity), where p(j) is the j-th prime. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 07 2006
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EXAMPLE
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Partitions of 9 into primes are 2+2+2+3=3+3+3=2+2+5=2+7; thus a(9)=4+3+3+2=12.
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MAPLE
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g:=sum(x^ithprime(j)/(1-x^ithprime(j)), j=1..20)/product(1-x^ithprime(j), j=1..20): gser:=series(g, x=0, 60): seq(coeff(gser, x^n), n=1..57); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 07 2006
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CROSSREFS
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Cf. A000607, A024938.
Sequence in context: A026317 A008768 A067593 this_sequence A046966 A035948 A094873
Adjacent sequences: A084990 A084991 A084992 this_sequence A084994 A084995 A084996
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KEYWORD
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nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)Eunet.yu), Jul 17 2003
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