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A325701
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Nonprime Heinz numbers of integer partitions whose reciprocal factorial sum is the reciprocal of an integer.
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0
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1, 9, 25, 49, 77, 121, 125, 169, 221, 245, 289, 323, 343, 361, 375, 437, 529, 841, 899, 961, 1331, 1369, 1517, 1681, 1763, 1849, 1859, 2021, 2197, 2209, 2401, 2773, 2809, 2873, 3127, 3481, 3721, 3757, 4087, 4489, 4757, 4913, 5041, 5183, 5329, 5929, 6137, 6241
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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: {}
9: {2,2}
25: {3,3}
49: {4,4}
77: {4,5}
121: {5,5}
125: {3,3,3}
169: {6,6}
221: {6,7}
245: {3,4,4}
289: {7,7}
323: {7,8}
343: {4,4,4}
361: {8,8}
375: {2,3,3,3}
437: {8,9}
529: {9,9}
841: {10,10}
899: {10,11}
961: {11,11}
For example, the sequence contains 245 because the prime indices of 245 are {3,4,4}, with reciprocal sum 1/6 + 1/24 + 1/24 = 1/4.
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MATHEMATICA
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Select[Range[1000], !PrimeQ[#]&&IntegerQ[1/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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