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Search: id:A121304
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| A121304 |
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Number of parts in all the compositions of n into primes (i.e. in all ordered sequences of primes having sum n). |
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+0
2
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| 1, 1, 2, 5, 5, 14, 17, 32, 53, 76, 139, 198, 334, 515, 798, 1280, 1938, 3075, 4710, 7299, 11298, 17296, 26738, 40874, 62763, 96036, 146674, 224210, 341562, 520767, 792375, 1204951, 1831124, 2779234, 4217008, 6391663, 9683056, 14659038, 22177341
(list; graph; listen)
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OFFSET
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2,3
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COMMENT
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a(n)=Sum(k*A121303(n,k), k=1..floor(n/2)).
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FORMULA
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g.f.=Sum(z^prime(i),i=1..infinity)/[1-Sum(z^prime(i),i=1..infinity)]^2.
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EXAMPLE
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a(8)=17 because the compositions of 8 into primes are [3,5], [5,3], [2,3,3], [3,2,3], [3,3,2] and [2,2,2,2], having a total of 2+2+3+3+3+4=17 parts.
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MAPLE
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g:=sum(z^ithprime(i), i=1..53)/(1-sum(z^ithprime(i), i=1..53))^2: gser:=series(g, z=0, 48): seq(coeff(gser, z, n), n=2..45);
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CROSSREFS
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Cf. A121303.
Sequence in context: A154696 A154698 A063786 this_sequence A002106 A064630 A089793
Adjacent sequences: A121301 A121302 A121303 this_sequence A121305 A121306 A121307
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 06 2006
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