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%I #4 Sep 20 2019 08:57:03
%S 1,2,2,3,2,4,2,4,2,4,2,6,2,4,4,5,2,4,2,6,3,4,2,8,2,4,2,6,2,8,2,6,4,4,
%T 4,6,2,4,3,8,2,6,2,6,4,4,2,10,2,4,4,6,2,4,4,8,3,4,2,12,2,4,3,7,3,8,2,
%U 6,4,8,2,8,2,4,4,6,4,6,2,10,2,4,2,9,4,4
%N Number of divisors of n that are 1, prime, or whose prime indices are pairwise coprime.
%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 prime or whose prime indices are pairwise coprime are listed in A302569.
%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, prime, or whose prime indices are pairwise coprime are {1, 2, 3, 4, 6, 7, 12, 14, 28}, so a(84) = 9.
%t primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t Table[Length[Select[Divisors[n],#==1||PrimeQ[#]||CoprimeQ@@primeMS[#]&]],{n,100}]
%Y See link for additional cross-references.
%Y Cf. A000005, A006530, A033273, A056239, A112798, A302569, A304711, A327513.
%K nonn
%O 1,2
%A _Gus Wiseman_, Sep 20 2019
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