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A327656 Maximum divisor of n that is 1 or whose prime indices have a common divisor > 1. 6

%I #11 Dec 06 2021 11:01:14

%S 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 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 11,7,57,29,59,5,61,31,63,1,65,11,67,17,23,7,71,9,73

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

%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. Numbers whose prime indices have a common divisor > 1 are listed in A318978, which is the union of this sequence without 1.

%H Antti Karttunen, <a href="/A327656/b327656.txt">Table of n, a(n) for n = 1..20000</a>

%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>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%F a(n) = n/A327405(n).

%F n belongs to A318978 iff a(n) = 1.

%e 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 Table[Max[Select[Divisors[n],GCD@@PrimePi/@First/@FactorInteger[#]!=1&]],{n,100}]

%o (PARI) A327656(n) = vecmax(select(d -> (1==d)||(gcd(apply(primepi,factor(d)[, 1]~))>1), divisors(n))); \\ _Antti Karttunen_, Dec 06 2021

%Y The union consists of {1} followed by A318978.

%Y See link for additional cross-references.

%Y Cf. A000005, A006530, A056239, A112798, A281116, A289509, A327406, A327657.

%K nonn

%O 1,3

%A _Gus Wiseman_, Sep 21 2019

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Last modified March 28 08:02 EDT 2024. Contains 371236 sequences. (Running on oeis4.)