A327391 Number of divisors of n that are 1, prime, or whose prime indices are pairwise coprime.

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, 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, 6, 4, 8, 2, 8, 2, 4, 4, 6, 4, 6, 2, 10, 2, 4, 2, 9, 4, 4

Offset: 1

Author

Gus Wiseman, Sep 20 2019

Keywords

• nonn

Comments

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.

Examples

			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.
		

Links

• Gus Wiseman, Sequences counting and encoding certain classes of multisets

Crossrefs

See link for additional cross-references.

Cf. A000005, A006530, A033273, A056239, A112798, A302569, A304711, A327513.

Programs

Mathematica

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Table[Length[Select[Divisors[n],#==1||PrimeQ[#]||CoprimeQ@@primeMS[#]&]],{n,100}]