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A282064
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Expansion of (x + Sum_{p prime, k>=1} x^(p^k))^3.
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13
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0, 0, 0, 1, 3, 6, 10, 15, 18, 22, 27, 33, 37, 45, 48, 52, 54, 60, 60, 69, 69, 79, 81, 87, 79, 93, 87, 97, 99, 114, 99, 120, 111, 130, 126, 150, 135, 168, 141, 160, 147, 177, 144, 189, 156, 183, 162, 201, 157, 213, 171, 214, 189, 231, 168, 237, 189, 244, 201, 261, 177, 270, 201, 261, 210, 282, 192, 297, 216, 283, 228
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OFFSET
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0,5
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COMMENTS
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Number of ways to write n as an ordered sum of three prime powers (1 included).
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LINKS
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FORMULA
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G.f.: (x + Sum_{p prime, k>=1} x^(p^k))^3.
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EXAMPLE
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a(6) = 10 because we have [4, 1, 1], [3, 2, 1], [3, 1, 2], [2, 3, 1], [2, 2, 2], [2, 1, 3], [1, 4, 1], [1, 3, 2], [1, 2, 3] and [1, 1, 4].
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MATHEMATICA
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nmax = 70; CoefficientList[Series[(x + Sum[Floor[1/PrimeNu[k]] x^k, {k, 2, nmax}])^3, {x, 0, nmax}], x]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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