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A236937
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Number of partitions of n such that the parts include all primes, with multiplicity, dividing n.
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3
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1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 3, 1, 7, 1, 7, 15, 22, 1, 42, 1, 56, 56, 30, 1, 176, 176, 56, 385, 297, 1, 627, 1, 1002, 490, 176, 1255, 2436, 1, 297, 1255, 4565, 1, 5604, 1, 4565, 12310, 792, 1, 21637, 14883, 26015, 6842, 14883, 1, 63261, 31185, 63261, 14883
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OFFSET
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0,9
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LINKS
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EXAMPLE
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With n = 9, 9 = 3 * 3. Since 9 - (3 + 3) = 3, and the partitions of 3 are {(3), (2, 1) (1, 1, 1), the partitions of 9 that include (3, 3) are {(3, 3, 3), (3, 3, 2, 1), and (3, 3, 1, 1, 1), so a(9) = 3.
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MAPLE
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with(combinat):
a:= n-> numbpart(n-add(i[1]*i[2], i=ifactors(n)[2])):
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MATHEMATICA
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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