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A279412
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Expansion of Sum_{k>=1} prime(k)*x^prime(k)/(1 + x^prime(k)) * Product_{k>=1} (1 + x^prime(k)).
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0
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0, 2, 3, 0, 10, 0, 14, 8, 9, 20, 11, 24, 26, 28, 30, 48, 34, 72, 57, 80, 84, 88, 115, 120, 125, 156, 135, 168, 203, 180, 279, 224, 297, 306, 315, 396, 407, 418, 507, 480, 574, 630, 645, 748, 720, 828, 893, 960, 1029, 1150, 1122, 1300, 1378, 1458, 1650, 1624, 1824, 1856, 2065, 2220, 2379, 2480, 2646, 2816, 2925
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OFFSET
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1,2
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COMMENTS
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Sum of all parts of all partitions of n into distinct primes.
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LINKS
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FORMULA
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G.f.: Sum_{k>=1} prime(k)*x^prime(k)/(1 + x^prime(k)) * Product_{k>=1} (1 + x^prime(k)).
G.f.: x*f'(x), where f(x) = Product_{k>=1} (1 + x^prime(k)).
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EXAMPLE
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a(12) = 24 because we have [7, 5], [7, 3, 2] and 2*12 = 24.
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MATHEMATICA
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nmax = 65; Rest[CoefficientList[Series[Sum[Prime[k] x^Prime[k]/(1 + x^Prime[k]), {k, 1, nmax}] Product[1 + x^Prime[k], {k, 1, nmax}], {x, 0, nmax}], x]]
nmax = 65; Rest[CoefficientList[Series[x D[Product[1 + x^Prime[k], {k, 1, nmax}], x], {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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