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A327512 Maximum divisor of n that is 1, 2, or a nonprime number whose prime indices are pairwise coprime.

%I A327512 #11 Dec 07 2021 11:07:16
%S A327512 1,2,1,4,1,6,1,8,1,10,1,12,1,14,15,16,1,6,1,20,1,22,1,24,1,26,1,28,1,
%T A327512 30,1,32,33,34,35,12,1,38,1,40,1,14,1,44,15,46,1,48,1,10,51,52,1,6,55,
%U A327512 56,1,58,1,60,1,62,1,64,1,66,1,68,69,70,1,24,1,74
%N A327512 Maximum divisor of n that is 1, 2, or a nonprime number whose prime indices are pairwise coprime.
%C A327512 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, which is the union of this sequence.
%C A327512 a(n) is the greatest term of A302696 which divides n. - _Antti Karttunen_, Dec 06 2021
%H A327512 Antti Karttunen, <a href="/A327512/b327512.txt">Table of n, a(n) for n = 1..20000</a>
%H A327512 Gus Wiseman, <a href="https://docs.google.com/document/d/e/2PACX-1vSX9dPMGJhxB8rOknCGvOs6PiyhupdWNpqLsnphdgU6MEVqFBnWugAXidDhwHeKqZe_YnUqYeGOXsOk/pub">Sequences counting and encoding certain classes of multisets</a>
%H A327512 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%e A327512 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) = 24.
%t A327512 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A327512 Table[Max[Select[Divisors[n],#==1||CoprimeQ@@primeMS[#]&]],{n,100}]
%o A327512 (PARI)
%o A327512 isA302696(n) = if(isprimepower(n),!(n%2), if(!issquarefree(n>>valuation(n,2)), 0, my(pis=apply(primepi,factor(n)[,1])); (lcm(pis)==factorback(pis))));
%o A327512 A327512(n) = vecmax(select(isA302696,divisors(n))); \\ _Antti Karttunen_, Dec 06 2021
%Y A327512 See link for additional cross-references.
%Y A327512 Cf. A000005, A006530, A056239, A112798, A289509, A302569, A302696, A304711.
%K A327512 nonn
%O A327512 1,2
%A A327512 _Gus Wiseman_, Sep 19 2019