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A103264
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Number of partitions of n into distinct parts prime to 3, 5 and 7.
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0
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 5, 6, 7, 8, 8, 9, 9, 10, 11, 13, 14, 15, 16, 18, 19, 21, 23, 24, 26, 28, 31, 34, 37, 39, 42, 45, 49, 53, 56, 60, 64, 69, 75, 81, 86, 92, 98, 105, 113, 122, 130, 138, 147, 157, 168, 179, 191, 202, 215, 230, 246, 262, 279
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OFFSET
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0,12
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LINKS
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FORMULA
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G.f.: product_{k>0}((1+x^k)*(1+x^(15k))*(1+x^(21k))*(1+x^(35k)))/((1+x^(3k))*(1+x^(5k))*(1+x^(7k))*(1+x^(105k))).
a(n) ~ exp(4*Pi*sqrt(n/105)) / (sqrt(2) * 105^(1/4) * n^(3/4)). - Vaclav Kotesovec, Sep 07 2015
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EXAMPLE
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a(19)=5 because 19 = 17 + 2 = 16 + 2 + 1 = 13 + 4 + 2 = 11 + 8.
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MAPLE
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series(product((1+x^k)*(1+x^(15*k))*(1+x^(21*k))*(1+x^(35*k)))/((1+x^(3*k))*(1+x^(5*k))*(1+x^(7*k))*(1+x^(105*k))), k=1..100), x=0, 100);
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MATHEMATICA
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CoefficientList[ Series[ Product[(1 + x^k)(1 + x^(15k))(1 + x^(21k))(1 + x^(35k))/((1 + x^(3k))(1 + x^(5k))(1 + x^(7k))(1 + x^(105k))), {k, 100}], {x, 0, 73}], x] (* Robert G. Wilson v, Feb 22 2005 *)
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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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