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A325042
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Heinz numbers of integer partitions whose product of parts is one fewer than their sum.
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14
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4, 6, 10, 14, 18, 22, 26, 34, 38, 46, 58, 60, 62, 74, 82, 86, 94, 106, 118, 122, 134, 142, 146, 158, 166, 168, 178, 194, 202, 206, 214, 216, 218, 226, 254, 262, 274, 278, 298, 302, 314, 326, 334, 346, 358, 362, 382, 386, 394, 398, 400, 422, 446, 454, 458, 466
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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 numbers whose product of prime indices (A003963) is one fewer than their sum of prime indices (A056239).
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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:
4: {1,1}
6: {1,2}
10: {1,3}
14: {1,4}
18: {1,2,2}
22: {1,5}
26: {1,6}
34: {1,7}
38: {1,8}
46: {1,9}
58: {1,10}
60: {1,1,2,3}
62: {1,11}
74: {1,12}
82: {1,13}
86: {1,14}
94: {1,15}
106: {1,16}
118: {1,17}
122: {1,18}
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MATHEMATICA
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primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[1000], Times@@primeMS[#]==Total[primeMS[#]]-1&]
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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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