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A327514
Quotient of n over the maximum divisor of n that is 1, 2, or a nonprime number whose prime indices are pairwise coprime.
1
1, 1, 3, 1, 5, 1, 7, 1, 9, 1, 11, 1, 13, 1, 1, 1, 17, 3, 19, 1, 21, 1, 23, 1, 25, 1, 27, 1, 29, 1, 31, 1, 1, 1, 1, 3, 37, 1, 39, 1, 41, 3, 43, 1, 3, 1, 47, 1, 49, 5, 1, 1, 53, 9, 1, 1, 57, 1, 59, 1, 61, 1, 63, 1, 65, 1, 67, 1, 1, 1, 71, 3, 73, 1, 5, 1, 1, 3
OFFSET
1,3
COMMENTS
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 that are 1, 2, or a nonprime number whose prime indices are pairwise coprime are listed in A302696.
EXAMPLE
The divisors of 72 that are 1, 2, or nonprime numbers whose prime indices are pairwise coprime are: {1, 2, 4, 6, 8, 12, 24}, so a(72) = 72/24 = 3.
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Table[n/Max[Select[Divisors[n], #==1||CoprimeQ@@primeMS[#]&]], {n, 100}]
CROSSREFS
See link for additional cross-references.
Sequence in context: A274658 A274660 A327531 * A009001 A093178 A340086
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 19 2019
STATUS
approved