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A325131
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Heinz numbers of integer partitions where the set of distinct parts is disjoint from the set of distinct multiplicities.
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24
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1, 3, 4, 5, 7, 8, 11, 13, 15, 16, 17, 19, 21, 23, 25, 27, 29, 31, 32, 33, 35, 37, 39, 41, 43, 47, 49, 51, 53, 55, 57, 59, 61, 64, 65, 67, 69, 71, 73, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 100, 101, 103, 105, 107, 109, 111, 113, 115, 119, 121, 123, 127
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OFFSET
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1,2
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COMMENTS
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The enumeration of these partitions by sum is given by A114639.
The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), so these are numbers where the prime indices are disjoint from the prime exponents.
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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: {}
3: {2}
4: {1,1}
5: {3}
7: {4}
8: {1,1,1}
11: {5}
13: {6}
15: {2,3}
16: {1,1,1,1}
17: {7}
19: {8}
21: {2,4}
23: {9}
25: {3,3}
27: {2,2,2}
29: {10}
31: {11}
32: {1,1,1,1,1}
33: {2,5}
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MATHEMATICA
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Select[Range[100], Intersection[PrimePi/@First/@FactorInteger[#], Last/@FactorInteger[#]]=={}&]
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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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