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A307825
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Number of partitions of n into 3 distinct prime powers (not including 1).
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4
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0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 4, 4, 5, 4, 6, 5, 7, 6, 8, 8, 10, 8, 10, 9, 12, 11, 12, 11, 15, 12, 15, 14, 17, 17, 20, 18, 19, 19, 19, 22, 23, 20, 21, 24, 23, 24, 24, 24, 27, 28, 24, 27, 28, 28, 28, 33, 27, 33, 29, 31, 30, 35, 27, 35, 33, 34, 31, 40, 32, 42, 35, 39, 35, 47, 32
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OFFSET
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0,13
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LINKS
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FORMULA
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a(n) = [x^n y^3] Product_{k>=1} (1 + y*x^A246655(k)).
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EXAMPLE
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a(15) = 4 because we have [9, 4, 2], [8, 5, 2], [8, 4, 3] and [7, 5, 3].
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MATHEMATICA
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Table[Count[IntegerPartitions[n, {3}], _?(And[UnsameQ @@ #, AllTrue[#, PrimePowerQ[#] &]] &)], {n, 0, 78}]
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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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