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A325621
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Heinz numbers of integer partitions whose reciprocal factorial sum is an integer.
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5
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1, 2, 4, 8, 9, 16, 18, 32, 36, 64, 72, 81, 128, 144, 162, 256, 288, 324, 375, 512, 576, 648, 729, 750, 1024, 1152, 1296, 1458, 1500, 2048, 2304, 2592, 2916, 3000, 3375, 4096, 4608, 5184, 5832, 6000, 6561, 6750, 8192, 9216, 10368, 11664, 12000, 13122, 13500
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OFFSET
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1,2
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COMMENTS
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The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
The reciprocal factorial sum of an integer partition (y_1,...,y_k) is 1/y_1! + ... + 1/y_k!.
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LINKS
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EXAMPLE
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The sequence of terms together with their prime indices begins:
1: {}
2: {1}
4: {1,1}
8: {1,1,1}
9: {2,2}
16: {1,1,1,1}
18: {1,2,2}
32: {1,1,1,1,1}
36: {1,1,2,2}
64: {1,1,1,1,1,1}
72: {1,1,1,2,2}
81: {2,2,2,2}
128: {1,1,1,1,1,1,1}
144: {1,1,1,1,2,2}
162: {1,2,2,2,2}
256: {1,1,1,1,1,1,1,1}
288: {1,1,1,1,1,2,2}
324: {1,1,2,2,2,2}
375: {2,3,3,3}
512: {1,1,1,1,1,1,1,1,1}
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MATHEMATICA
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Select[Range[1000], IntegerQ[Total[Cases[FactorInteger[#], {p_, k_}:>k/PrimePi[p]!]]]&]
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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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