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A371283
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Heinz numbers of sets of divisors of positive integers. Numbers whose prime indices form the set of divisors of some positive integer.
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5
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2, 6, 10, 22, 34, 42, 62, 82, 118, 134, 166, 218, 230, 254, 314, 358, 382, 390, 422, 482, 554, 566, 662, 706, 734, 798, 802, 862, 922, 1018, 1094, 1126, 1174, 1198, 1234, 1418, 1478, 1546, 1594, 1718, 1754, 1838, 1914, 1934, 1982, 2062, 2126, 2134, 2174, 2306
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OFFSET
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1,1
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COMMENTS
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The Heinz number of a partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). This gives a bijective correspondence between positive integers and integer partitions.
A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
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LINKS
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EXAMPLE
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The terms together with their prime indices begin:
2: {1}
6: {1,2}
10: {1,3}
22: {1,5}
34: {1,7}
42: {1,2,4}
62: {1,11}
82: {1,13}
118: {1,17}
134: {1,19}
166: {1,23}
218: {1,29}
230: {1,3,9}
254: {1,31}
314: {1,37}
358: {1,41}
382: {1,43}
390: {1,2,3,6}
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MATHEMATICA
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prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[2, 100], SameQ[prix[#], Divisors[Last[prix[#]]]]&]
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CROSSREFS
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Partitions of this type are counted by A054973.
A001221 counts distinct prime factors.
A355731 counts choices of a divisor of each prime index, firsts A355732.
A355741 counts choices of a prime factor of each prime index.
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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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