cp's OEIS Frontend

A327401 Quotient of n over the maximum divisor of n that is 1, prime, or whose prime indices are pairwise coprime.

%I A327401 #7 Sep 20 2019 08:57:12
%S A327401 1,1,1,1,1,1,1,1,3,1,1,1,1,1,1,1,1,3,1,1,3,1,1,1,5,1,9,1,1,1,1,1,1,1,
%T A327401 1,3,1,1,3,1,1,3,1,1,3,1,1,1,7,5,1,1,1,9,1,1,3,1,1,1,1,1,9,1,5,1,1,1,
%U A327401 1,1,1,3,1,1,5,1,1,3,1,1,27,1,1,3,1,1,3
%N A327401 Quotient of n over the maximum divisor of n that is 1, prime, or whose prime indices are pairwise coprime.
%C A327401 All terms are odd.
%C A327401 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 > 1 that are prime or whose prime indices are pairwise coprime are listed in A302569.
%H A327401 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 A327401 The divisors of 84 that are 1, prime, or whose prime indices are pairwise coprime are {1, 2, 3, 4, 6, 7, 12, 14, 28}, so a(84) = 84/28 = 3.
%t A327401 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A327401 Table[n/Max[Select[Divisors[n],#==1||PrimeQ[#]||CoprimeQ@@primeMS[#]&]],{n,100}]
%Y A327401 See link for additional cross-references.
%Y A327401 Cf. A000005, A006530, A056239, A112798, A302569, A304711.
%K A327401 nonn
%O A327401 1,9
%A A327401 _Gus Wiseman_, Sep 20 2019