A327530 - OEIS

%I #7 Sep 19 2019 21:49:16

%S 1,2,1,3,1,3,1,4,1,3,1,5,1,3,2,5,1,4,1,5,1,3,1,7,1,3,1,5,1,6,1,6,2,3,

%T 2,7,1,3,1,7,1,5,1,5,3,3,1,9,1,4,2,5,1,5,2,7,1,3,1,10,1,3,1,7,1,6,1,5,

%U 2,6,1,10,1,3,3,5,2,5,1,9,1,3,1,9,2,3

%N Number of divisors of n that are 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 maximum divisor of n that is 1 or whose prime indices are relatively prime is A327529(n).

%H Robert Israel, <a href="/A327530/b327530.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>

%e The divisors of 84 that are 1 or whose prime indices are relatively prime are {1, 2, 4, 6, 12, 14, 28, 42, 84}, so a(84) = 9.

%p N:= 100: # for a(1)..a(N)

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

%p V:= Vector(N,1):

%p for k in select(g, [$2..N]) do

%p   R:=[seq(i,i=k..N,k)]:

%p   V[R]:= map(`+`,V[R],1);

%p od:

%p convert(V,list); # _Robert Israel_, Sep 19 2019

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

%Y See link for additional cross-references.

%Y Cf. A000005, A006530, A112798, A281116, A289509, A318721.

%K nonn

%O 1,2

%A _Gus Wiseman_, Sep 17 2019