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, 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.

Links

Table of n, a(n) for n=1..78.

Gus Wiseman, Sequences counting and encoding certain classes of multisets

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.

Cf. A000005, A006530, A056239, A112798, A302569, A302696, A304711.

Sequence in context: A274658 A274660 A327531 * A009001 A093178 A340086

Adjacent sequences: A327511 A327512 A327513 * A327515 A327516 A327517

Keyword

nonn

Author

Gus Wiseman, Sep 19 2019

Status

approved