A327393 - OEIS

%I #7 Sep 16 2019 12:38:15

%S 1,2,3,4,5,3,7,8,9,5,11,4,13,7,15,16,17,9,19,5,7,11,23,8,25,13,27,7,

%T 29,15,31,32,33,17,35,9,37,19,13,8,41,7,43,11,45,23,47,16,49,25,51,13,

%U 53,27,55,8,19,29,59,15,61,31,9,64,13,33,67,17,69,35,71

%N Maximum stable divisor of n.

%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. A number is stable if its distinct prime indices are pairwise indivisible. Stable numbers are listed in A316476, which is the union of this sequence without 1.

%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 stable divisors of 60 are {1, 2, 3, 4, 5, 15}, so a(60) = 15.

%t stableQ[u_,Q_]:=!Apply[Or,Outer[#1=!=#2&&Q[#1,#2]&,u,u,1],{0,1}];

%t Table[Max[Select[Divisors[n],stableQ[PrimePi/@First/@FactorInteger[#],Divisible]&]],{n,100}]

%Y See link for additional cross-references.

%Y Cf. A000005, A006530, A302242, A303362.

%K nonn

%O 1,2

%A _Gus Wiseman_, Sep 15 2019