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A327502
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a(n) = n/A327501(n), where A327501(n) is the maximum divisor of n that is 1 or not a perfect power.
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4
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1, 1, 1, 2, 1, 1, 1, 4, 3, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 9, 1, 1, 1, 1, 16, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 32, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 27, 1, 1, 1, 1, 1
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OFFSET
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1,4
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COMMENTS
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This maximum divisor is given by A327501.
A multiset is aperiodic if its multiplicities are relatively prime. The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). Heinz numbers of aperiodic multisets are numbers that are not perfect powers (A007916).
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LINKS
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FORMULA
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EXAMPLE
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The divisors of 36 that are 1 or not a perfect power are {1, 2, 3, 6, 12, 18}, so a(36) = 36/18 = 2.
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MATHEMATICA
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Table[n/Max[Select[Divisors[n], GCD@@Last/@FactorInteger[#]==1&]], {n, 100}]
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PROG
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CROSSREFS
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See link for additional cross-references.
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KEYWORD
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AUTHOR
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STATUS
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approved
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