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A327401
Quotient of n over the maximum divisor of n that is 1, prime, or whose prime indices are pairwise coprime.
1
1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 1, 5, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 1, 7, 5, 1, 1, 1, 9, 1, 1, 3, 1, 1, 1, 1, 1, 9, 1, 5, 1, 1, 1, 1, 1, 1, 3, 1, 1, 5, 1, 1, 3, 1, 1, 27, 1, 1, 3, 1, 1, 3
OFFSET
1,9
COMMENTS
All terms are odd.
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 > 1 that are prime or whose prime indices are pairwise coprime are listed in A302569.
EXAMPLE
The divisors of 84 that are 1, prime, or whose prime indices are pairwise coprime are {1, 2, 3, 4, 6, 7, 12, 14, 28}, so a(84) = 84/28 = 3.
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Table[n/Max[Select[Divisors[n], #==1||PrimeQ[#]||CoprimeQ@@primeMS[#]&]], {n, 100}]
CROSSREFS
See link for additional cross-references.
Sequence in context: A356306 A355931 A031178 * A091407 A031229 A031228
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 20 2019
STATUS
approved