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A327656 Maximum divisor of n that is 1 or whose prime indices have a common divisor > 1.

%I A327656 #11 Dec 06 2021 11:01:14
%S A327656 1,1,3,1,5,3,7,1,9,5,11,3,13,7,5,1,17,9,19,5,21,11,23,3,25,13,27,7,29,
%T A327656 5,31,1,11,17,7,9,37,19,39,5,41,21,43,11,9,23,47,3,49,25,17,13,53,27,
%U A327656 11,7,57,29,59,5,61,31,63,1,65,11,67,17,23,7,71,9,73
%N A327656 Maximum divisor of n that is 1 or whose prime indices have a common divisor > 1.
%C A327656 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 whose prime indices have a common divisor > 1 are listed in A318978, which is the union of this sequence without 1.
%H A327656 Antti Karttunen, <a href="/A327656/b327656.txt">Table of n, a(n) for n = 1..20000</a>
%H A327656 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 A327656 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A327656 a(n) = n/A327405(n).
%F A327656 n belongs to A318978 iff a(n) = 1.
%e A327656 The divisors of 90 that are 1 or whose prime indices have a common divisor > 1 are {1, 3, 5, 9}, so a(90) = 9.
%t A327656 Table[Max[Select[Divisors[n],GCD@@PrimePi/@First/@FactorInteger[#]!=1&]],{n,100}]
%o A327656 (PARI) A327656(n) = vecmax(select(d -> (1==d)||(gcd(apply(primepi,factor(d)[, 1]~))>1), divisors(n))); \\ _Antti Karttunen_, Dec 06 2021
%Y A327656 The union consists of {1} followed by A318978.
%Y A327656 See link for additional cross-references.
%Y A327656 Cf. A000005, A006530, A056239, A112798, A281116, A289509, A327406, A327657.
%K A327656 nonn
%O A327656 1,3
%A A327656 _Gus Wiseman_, Sep 21 2019