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

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%I A327404 #4 Sep 24 2019 12:39:12
%S A327404 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,
%T A327404 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,
%U A327404 4,3,10,1,8,1,2,3,4,7,2,1,16,1,2,1,4,5
%N A327404 Quotient of n over the maximum divisor of n that is 2 or whose prime indices have a common divisor > 1.
%C A327404 First differs from A327395 at a(195) = 65, A327395(195) = 195.
%C A327404 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.
%H A327404 Gus Wiseman, <a href="https://docs.google.com/document/d/e/2PACX-1vSX9dPMGJhxB8rOknCGvOs6PiyhupdWNpqLsnphdgU6MEVqFBnWugAXidDhwHeKqZe_YnUqYeGOXsOk/pub">Sequences counting and encoding certain classes of multisets</a>
%e A327404 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.
%t A327404 Table[n/Max[Select[Divisors[n],#==2||GCD@@PrimePi/@First/@FactorInteger[#]!=1&]],{n,100}]
%Y A327404 See link for additional cross-references.
%Y A327404 Cf. A000005, A006530, A056239, A112798, A289509, A302569, A327407, A327656.
%K A327404 nonn
%O A327404 1,4
%A A327404 _Gus Wiseman_, Sep 23 2019