%I #5 Sep 18 2019 04:58:07
%S 1,2,2,3,2,4,2,4,2,4,2,6,2,4,4,5,2,5,2,6,3,4,2,8,2,4,2,6,2,8,2,6,4,4,
%T 4,8,2,4,3,8,2,7,2,6,5,4,2,10,2,5,4,6,2,6,4,8,3,4,2,12,2,4,3,7,3,8,2,
%U 6,4,8,2,11,2,4,5,6,4,7,2,10,2,4,2,11,4
%N Number of divisors of n that are 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 maximum divisor of n satisfying the same conditions is A327535(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>
%e The divisors of 63 that are 1, prime, or whose prime indices are relatively prime are {1, 3, 7}, so a(63) = 3.
%t Table[Length[Select[Divisors[n],#==1||PrimeQ[#]||GCD@@PrimePi/@First/@FactorInteger[#]==1&]],{n,100}]
%Y See link for additional cross-references.
%Y Cf. A000005, A056239, A112798, A281116, A289509, A327407.
%K nonn
%O 1,2
%A _Gus Wiseman_, Sep 17 2019