

A327405


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


2



1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 3, 16, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 6, 1, 32, 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, 64, 1, 6, 1, 4, 3, 10, 1, 8, 1, 2, 3, 4, 7, 2, 1, 16, 1, 2, 1, 4, 5
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OFFSET

1,2


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 whose prime indices have a common divisor > 1 are listed in A318978.


LINKS

Table of n, a(n) for n=1..85.
Gus Wiseman, Sequences counting and encoding certain classes of multisets


FORMULA

a(n) = n/A327656(n).


EXAMPLE

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


MATHEMATICA

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


CROSSREFS

See link for additional crossreferences.
Cf. A000005, A056239, A112798, A281116, A289509, A302569.
Sequence in context: A118830 A055975 A006519 * A322362 A087258 A333763
Adjacent sequences: A327402 A327403 A327404 * A327406 A327407 A327408


KEYWORD

nonn


AUTHOR

Gus Wiseman, Sep 21 2019


STATUS

approved



