%I #13 Dec 06 2021 10:57:01

%S 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,

%T 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,

%U 1,4,3,10,1,8,1,2,3,4,7,2,1,16,1,2,1,4,5

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

%C 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.

%H Antti Karttunen, <a href="/A327405/b327405.txt">Table of n, a(n) for n = 1..20000</a>

%H Gus Wiseman, <a href="https://docs.google.com/document/d/e/2PACX-1vSX9dPMGJhxB8rOknCGvOs6PiyhupdWNpqLsnphdgU6MEVqFBnWugAXidDhwHeKqZe_YnUqYeGOXsOk/pub">Sequences counting and encoding certain classes of multisets</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

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

%e 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.

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

%o (PARI) A327405(n) = (n / vecmax(select(d -> (1==d)||(gcd(apply(primepi,factor(d)[, 1]~))>1), divisors(n)))); \\ _Antti Karttunen_, Dec 06 2021

%Y See link for additional cross-references.

%Y Cf. A000005, A056239, A112798, A281116, A289509, A302569.

%K nonn,look

%O 1,2

%A _Gus Wiseman_, Sep 21 2019