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A327391
Number of divisors of n that are 1, prime, or whose prime indices are pairwise coprime.
0
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.
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.
Sequence in context: A093640 A320538 A343650 * A365207 A083903 A327536
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 20 2019
STATUS
approved