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A325761
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Heinz numbers of integer partitions whose length is itself a part.
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8
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1, 2, 6, 9, 15, 20, 21, 30, 33, 39, 45, 50, 51, 56, 57, 69, 70, 75, 84, 87, 93, 105, 110, 111, 123, 125, 126, 129, 130, 140, 141, 159, 165, 170, 175, 176, 177, 183, 189, 190, 195, 196, 201, 210, 213, 219, 230, 237, 245, 249, 255, 264, 267, 275, 285, 290, 291
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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 enumeration of these partitions by sum is given by A002865.
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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}
6: {1,2}
9: {2,2}
15: {2,3}
20: {1,1,3}
21: {2,4}
30: {1,2,3}
33: {2,5}
39: {2,6}
45: {2,2,3}
50: {1,3,3}
51: {2,7}
56: {1,1,1,4}
57: {2,8}
69: {2,9}
70: {1,3,4}
75: {2,3,3}
84: {1,1,2,4}
87: {2,10}
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MATHEMATICA
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Select[Range[100], MemberQ[PrimePi/@First/@FactorInteger[#], PrimeOmega[#]]&]
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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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