A327529 - OEIS

%I #11 Sep 19 2019 22:43:48

%S 1,2,1,4,1,6,1,8,1,10,1,12,1,14,15,16,1,18,1,20,1,22,1,24,1,26,1,28,1,

%T 30,1,32,33,34,35,36,1,38,1,40,1,42,1,44,45,46,1,48,1,50,51,52,1,54,

%U 55,56,1,58,1,60,1,62,1,64,1,66,1,68,69,70,1,72,1,74

%N Maximum divisor of n that is 1 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 whose prime indices are relatively prime are A289509. The number of divisors of n that are 1 or whose prime indices are relatively prime is A327530(n).

%H Robert Israel, <a href="/A327529/b327529.txt">Table of n, a(n) for n = 1..10000</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>

%F a(n) = n if n is in A289509, otherwise a(n) = 1.

%p g:= proc(n)  uses numtheory; igcd(op(map(pi,factorset(n))))=1 end proc:

%p seq(`if`(g(n),n,1), n=1..100); # _Robert Israel_, Sep 19 2019

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

%Y See link for additional cross-references.

%Y Cf. A000005, A112798, A281116, A289509, A318721.

%K nonn

%O 1,2

%A _Gus Wiseman_, Sep 17 2019