A327404 Quotient of n over the maximum divisor of n that is 2 or whose prime indices have a common divisor > 1.

1, 1, 1, 2, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 3, 8, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 6, 1, 16, 3, 2, 5, 4, 1, 2, 1, 8, 1, 2, 1, 4, 5, 2, 1, 16, 1, 2, 3, 4, 1, 2, 5, 8, 1, 2, 1, 12, 1, 2, 1, 32, 1, 6, 1, 4, 3, 10, 1, 8, 1, 2, 3, 4, 7, 2, 1, 16, 1, 2, 1, 4, 5

Offset: 1

Author

Gus Wiseman, Sep 23 2019

Keywords

• nonn

Comments

First differs from A327395 at a(195) = 65, A327395(195) = 195.

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.

Examples

			The divisors of 90 that are 2 or whose prime indices have a common divisor > 1 are {1, 2, 3, 5, 9}, so a(90) = 90/9 = 10.
		

Links

• Gus Wiseman, Sequences counting and encoding certain classes of multisets

Crossrefs

See link for additional cross-references.

Cf. A000005, A006530, A056239, A112798, A289509, A302569, A327407, A327656.

Programs

Mathematica

Table[n/Max[Select[Divisors[n],#==2||GCD@@PrimePi/@First/@FactorInteger[#]!=1&]],{n,100}]