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A143773
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Number of partitions of n such that every part is divisible by number of parts.
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54
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1, 1, 1, 2, 1, 2, 1, 3, 2, 3, 1, 5, 1, 4, 3, 6, 1, 8, 1, 7, 5, 6, 1, 14, 2, 7, 8, 11, 1, 17, 1, 14, 11, 9, 3, 29, 1, 10, 15, 23, 1, 28, 1, 23, 25, 12, 1, 51, 2, 20, 25, 32, 1, 44, 11, 39, 31, 15, 1, 94, 1, 16, 40, 52, 19, 64, 1, 57, 45, 44, 1, 126, 1, 19, 83, 74, 6, 90, 1, 124, 63, 21, 1, 186
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OFFSET
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1,4
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LINKS
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FORMULA
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G.f.: Sum(x^(k^2)/Product(1-x^(k*i), i=1..k), k=1..infinity).
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EXAMPLE
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The a(18) = 8 partitions are (18), (10 8), (12 6), (14 4), (16 2), (6 6 6), (9 6 3), (12 3 3). - Gus Wiseman, Jan 26 2018
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MATHEMATICA
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m = 100;
gf = Sum[x^(k^2)/Product[1-x^(k*i), {i, 1, k}], {k, 1, Sqrt[m]//Ceiling}];
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PROG
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(PARI) Vec(sum(k=1, 20, x^(k^2)/prod(i=1, k, 1-x^(k*i)+O(x^400)))) \\ Max Alekseyev, May 03 2009
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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