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A327656
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Maximum divisor of n that is 1 or whose prime indices have a common divisor > 1.
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6
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1, 1, 3, 1, 5, 3, 7, 1, 9, 5, 11, 3, 13, 7, 5, 1, 17, 9, 19, 5, 21, 11, 23, 3, 25, 13, 27, 7, 29, 5, 31, 1, 11, 17, 7, 9, 37, 19, 39, 5, 41, 21, 43, 11, 9, 23, 47, 3, 49, 25, 17, 13, 53, 27, 11, 7, 57, 29, 59, 5, 61, 31, 63, 1, 65, 11, 67, 17, 23, 7, 71, 9, 73
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OFFSET
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1,3
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COMMENTS
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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. Numbers whose prime indices have a common divisor > 1 are listed in A318978, which is the union of this sequence without 1.
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LINKS
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FORMULA
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EXAMPLE
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The divisors of 90 that are 1 or whose prime indices have a common divisor > 1 are {1, 3, 5, 9}, so a(90) = 9.
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MATHEMATICA
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Table[Max[Select[Divisors[n], GCD@@PrimePi/@First/@FactorInteger[#]!=1&]], {n, 100}]
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PROG
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(PARI) A327656(n) = vecmax(select(d -> (1==d)||(gcd(apply(primepi, factor(d)[, 1]~))>1), divisors(n))); \\ Antti Karttunen, Dec 06 2021
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CROSSREFS
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The union consists of {1} followed by A318978.
See link for additional cross-references.
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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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