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Search: id:A111865
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| A111865 |
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Number of partitions of n into parts size sigma(k) over all k. |
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+0
1
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| 1, 1, 2, 3, 3, 5, 7, 9, 11, 14, 17, 24, 29, 36, 46, 57, 66, 85, 103, 125, 151, 182, 213, 264, 310, 368, 440, 524, 604, 724, 849, 998, 1164, 1363, 1573, 1854, 2136, 2481, 2879, 3336, 3807, 4427, 5079, 5844, 6698, 7695, 8754, 10072, 11451, 13075, 14898, 16988
(list; graph; listen)
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OFFSET
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1,3
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FORMULA
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G.f.: product[k=1, oo, 1/(1-x^sigma(k)]
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EXAMPLE
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a(6) = 5 : We have sigma(1)=1, sigma(2)=3, sigma(3)=4, sigma(5)=6 so 111111, 1113, 114, 6 and 33.
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MATHEMATICA
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Rest[ CoefficientList[ Series[Product[1/(1 - x^DivisorSigma[1, k]), {k, 47}], {x, 0, 52}], x]] (* Robert G. Wilson v *).
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CROSSREFS
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Adjacent sequences: A111862 A111863 A111864 this_sequence A111866 A111867 A111868
Sequence in context: A027587 A030729 A030779 this_sequence A042955 A035553 A108961
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KEYWORD
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nonn
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AUTHOR
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Jon Perry (perry(AT)globalnet.co.uk), Nov 23 2005
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(at)rgwv.com), Nov 25 2005
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