A327404 - OEIS

%I #4 Sep 24 2019 12:39:12

%S 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 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 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 2 or whose prime indices have a common divisor > 1.

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

%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.

%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>

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

%Y See link for additional cross-references.

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

%K nonn

%O 1,4

%A _Gus Wiseman_, Sep 23 2019