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A325259
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Numbers with one fewer distinct prime exponents than distinct prime factors.
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6
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6, 10, 14, 15, 21, 22, 26, 33, 34, 35, 36, 38, 39, 46, 51, 55, 57, 58, 60, 62, 65, 69, 74, 77, 82, 84, 85, 86, 87, 90, 91, 93, 94, 95, 100, 106, 111, 115, 118, 119, 120, 122, 123, 126, 129, 132, 133, 134, 140, 141, 142, 143, 145, 146, 150, 155, 156, 158, 159
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OFFSET
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1,1
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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), so these are Heinz numbers of integer partitions with one fewer distinct multiplicities than distinct parts. The enumeration of these partitions by sum is given by A325244.
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LINKS
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FORMULA
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EXAMPLE
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The sequence of terms together with their prime indices begins:
6: {1,2}
10: {1,3}
14: {1,4}
15: {2,3}
21: {2,4}
22: {1,5}
26: {1,6}
33: {2,5}
34: {1,7}
35: {3,4}
36: {1,1,2,2}
38: {1,8}
39: {2,6}
46: {1,9}
51: {2,7}
55: {3,5}
57: {2,8}
58: {1,10}
60: {1,1,2,3}
62: {1,11}
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MATHEMATICA
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Select[Range[100], PrimeNu[#]==Length[Union[Last/@FactorInteger[#]]]+1&]
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CROSSREFS
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Cf. A056239, A060687, A090858, A112798, A116608, A118914, A130091, A323023, A325241, A325242, A325244, A325270, A325281.
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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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