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A319071
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Number of integer partitions of n whose product of parts is a perfect power and whose parts all have the same number of prime factors, counted with multiplicity.
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7
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1, 0, 0, 0, 2, 0, 2, 0, 3, 2, 3, 0, 4, 1, 4, 3, 7, 1, 7, 1, 8, 6, 8, 0, 15, 5, 12, 6, 15, 4, 22, 4, 24, 12, 22, 8, 35, 7, 30, 16, 42, 9, 50, 9, 50, 30, 53, 7, 79, 22, 72, 33, 87, 21, 109, 26, 111, 55, 117, 24, 168, 40, 149, 65, 178, 59
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OFFSET
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0,5
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COMMENTS
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The positions of zeros appear to be A048278.
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LINKS
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EXAMPLE
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The a(4) = 2 through a(16) = 7 integer partitions (G = 16):
4 33 8 9 55 66 94 77 555 G
22 222 44 333 3322 444 5522 33333 88
2222 22222 3333 332222 333222 664
222222 2222222 4444
5533
333322
22222222
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], And[GCD@@FactorInteger[Times@@#][[All, 2]]>1, SameQ@@PrimeOmega/@#]&]], {n, 30}]
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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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