cp's OEIS Frontend

A327514 Quotient of n over the maximum divisor of n that is 1, 2, or a nonprime number whose prime indices are pairwise coprime.

%I A327514 #4 Sep 20 2019 08:57:47
%S A327514 1,1,3,1,5,1,7,1,9,1,11,1,13,1,1,1,17,3,19,1,21,1,23,1,25,1,27,1,29,1,
%T A327514 31,1,1,1,1,3,37,1,39,1,41,3,43,1,3,1,47,1,49,5,1,1,53,9,1,1,57,1,59,
%U A327514 1,61,1,63,1,65,1,67,1,1,1,71,3,73,1,5,1,1,3
%N A327514 Quotient of n over the maximum divisor of n that is 1, 2, or a nonprime number whose prime indices are pairwise coprime.
%C A327514 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 that are 1, 2, or a nonprime number whose prime indices are pairwise coprime are listed in A302696.
%H A327514 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 A327514 The divisors of 72 that are 1, 2, or nonprime numbers whose prime indices are pairwise coprime are: {1, 2, 4, 6, 8, 12, 24}, so a(72) = 72/24 = 3.
%t A327514 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A327514 Table[n/Max[Select[Divisors[n],#==1||CoprimeQ@@primeMS[#]&]],{n,100}]
%Y A327514 See link for additional cross-references.
%Y A327514 Cf. A000005, A006530, A056239, A112798, A302569, A302696, A304711.
%K A327514 nonn
%O A327514 1,3
%A A327514 _Gus Wiseman_, Sep 19 2019