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, 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.

Links

Table of n, a(n) for n=1..87.

Gus Wiseman, Sequences counting and encoding certain classes of multisets

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.

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

Sequence in context: A356306 A355931 A031178 * A091407 A031229 A031228

Adjacent sequences: A327398 A327399 A327400 * A327402 A327403 A327404

Keyword

nonn

Author

Gus Wiseman, Sep 20 2019

Status

approved