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Maximum divisor of n that is 1, prime, or whose prime indices are relatively prime.
3

%I #5 Sep 18 2019 04:57:59

%S 1,2,3,4,5,6,7,8,3,10,11,12,13,14,15,16,17,18,19,20,7,22,23,24,5,26,3,

%T 28,29,30,31,32,33,34,35,36,37,38,13,40,41,42,43,44,45,46,47,48,7,50,

%U 51,52,53,54,55,56,19,58,59,60,61,62,7,64,13,66,67,68,69

%N Maximum divisor of n that is 1, prime, or whose prime indices are relatively prime.

%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 that are 1, prime, or whose prime indices are relatively prime are A327534. The number of divisors of n satisfying the same conditions is A327536(n).

%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>

%F If n is in A327534, then a(n) = n; otherwise a(n) = A006530(n).

%e The divisors of 63 that are 1, prime, or whose prime indices are relatively prime are {1, 3, 7}, so a(63) = 7.

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

%Y See link for additional cross-references.

%Y Cf. A000005, A000961, A006530, A056239, A112798, A281116, A289509, A327407.

%K nonn

%O 1,2

%A _Gus Wiseman_, Sep 17 2019