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A358103
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Quotient of the n-th divisible pair, where pairs are ordered by Heinz number. Quotient of prime indices of A318990(n).
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6
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1, 2, 1, 3, 4, 2, 5, 1, 6, 7, 8, 3, 9, 1, 4, 10, 11, 2, 12, 13, 14, 5, 15, 16, 6, 3, 17, 1, 18, 7, 2, 19, 20, 21, 22, 8, 23, 1, 24, 9, 4, 25, 26, 27, 10, 28, 29, 30, 5, 11, 31, 3, 32, 12, 33, 34, 1, 35, 36, 13, 6, 37, 2, 14, 38, 39, 15, 40, 41, 1, 42, 7, 4, 43
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OFFSET
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1,2
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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.
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LINKS
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FORMULA
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EXAMPLE
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The 12th divisible pair is (2,6) so a(12) = 3.
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MATHEMATICA
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primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Join@@Table[Cases[primeMS[n], {x_, y_}/; Divisible[y, x]:>y/x, {0}], {n, 100}]
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CROSSREFS
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A003963 multiplies together prime indices.
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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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