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A327657
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Number of divisors of n that are 1 or whose prime indices have a common divisor > 1.
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3
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1, 1, 2, 1, 2, 2, 2, 1, 3, 2, 2, 2, 2, 2, 3, 1, 2, 3, 2, 2, 4, 2, 2, 2, 3, 2, 4, 2, 2, 3, 2, 1, 3, 2, 3, 3, 2, 2, 4, 2, 2, 4, 2, 2, 4, 2, 2, 2, 3, 3, 3, 2, 2, 4, 3, 2, 4, 2, 2, 3, 2, 2, 6, 1, 4, 3, 2, 2, 3, 3, 2, 3, 2, 2, 4, 2, 3, 4, 2, 2, 5, 2, 2, 4, 3, 2, 4, 2, 2, 4, 4, 2, 3, 2, 3, 2, 2, 3, 4, 3, 2, 3, 2, 2, 5
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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.
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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) = 4.
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MATHEMATICA
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Table[Length[Select[Divisors[n], GCD@@PrimePi/@First/@FactorInteger[#]!=1&]], {n, 100}]
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PROG
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(PARI) A327657(n) = sumdiv(n, d, (1==d)||(gcd(apply(x->primepi(x), factor(d)[, 1]))>1)); \\ Antti Karttunen, Dec 05 2021
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CROSSREFS
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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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EXTENSIONS
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STATUS
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approved
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