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Search: id:A024938
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| A024938 |
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Total number of parts in all partitions of n into distinct prime parts. |
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+0
2
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| 0, 1, 1, 0, 3, 0, 3, 2, 2, 5, 1, 5, 3, 5, 5, 7, 5, 10, 6, 10, 12, 10, 15, 12, 16, 17, 17, 19, 22, 17, 27, 21, 30, 30, 31, 35, 36, 40, 45, 45, 49, 53, 50, 62, 60, 69, 69, 73, 78, 85, 88, 98, 100, 105, 116, 116, 134, 135, 141, 149, 154, 168, 176, 188, 195, 206, 211, 232, 242, 255, 267, 276
(list; graph; listen)
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OFFSET
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1,5
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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. - Vladeta Jovovic
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EXAMPLE
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a(16)=7 because the partitions of 16 into distinct prime parts are [13,3],[11,5] and [11,3,2].
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MAPLE
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g:=sum(x^ithprime(j)/(1+x^ithprime(j)), j=1..30)*product(1+x^ithprime(j), j=1..30): gser:=series(g, x=0, 80): seq(coeff(gser, x, n), n=1..75); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 01 2006
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MATHEMATICA
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Rest@ CoefficientList[ Series[ Sum[x^Prime@j/(1 + x^Prime@j), {j, 20}]* Product[1 + x^Prime@j, {j, 20}], {x, 0, 70}], x] (* Robert G. Wilson v *)
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CROSSREFS
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Cf. A084993.
Sequence in context: A085919 A105824 A070298 this_sequence A004604 A016035 A112470
Adjacent sequences: A024935 A024936 A024937 this_sequence A024939 A024940 A024941
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KEYWORD
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easy,nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
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More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 17 2003
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