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

1,2

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.

Links

Table of n, a(n) for n=1..86.

Gus Wiseman, Sequences counting and encoding certain classes of multisets

Example

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.

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}]

Crossrefs

See link for additional cross-references.

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

Sequence in context: A093640 A320538 A343650 * A365207 A083903 A327536

Adjacent sequences: A327388 A327389 A327390 * A327392 A327393 A327394

Keyword

nonn

Author

Gus Wiseman, Sep 20 2019

Status

approved