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A327657 Number of divisors of n that are 1 or whose prime indices have a common divisor > 1. 0
1, 1, 2, 1, 2, 2, 2, 1, 3, 2, 2, 2, 2, 2, 3, 1, 2, 3, 2, 2, 4, 2, 2, 2, 3, 2, 4, 2, 2, 3, 2, 1, 3, 2, 3, 3, 2, 2, 4, 2, 2, 4, 2, 2, 4, 2, 2, 2, 3, 3, 3, 2, 2, 4, 3, 2, 4, 2, 2, 3, 2, 2, 6, 1, 4, 3, 2, 2, 3, 3, 2, 3, 2, 2, 4, 2, 3, 4, 2, 2, 5, 2, 2, 4, 3, 2, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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 whose prime indices have a common divisor > 1 are listed in A318978.

LINKS

Table of n, a(n) for n=1..87.

Gus Wiseman, Sequences counting and encoding certain classes of multisets

EXAMPLE

The divisors of 90 that are 1 or whose prime indices have a common divisor > 1 are {1, 3, 5, 9}, so a(90) = 4.

MATHEMATICA

Table[Length[Select[Divisors[n], GCD@@PrimePi/@First/@FactorInteger[#]!=1&]], {n, 100}]

CROSSREFS

See link for additional cross-references.

Cf. A000005, A056239, A112798, A281116, A289509, A327406.

Sequence in context: A023588 A175242 A225843 * A301957 A318874 A001227

Adjacent sequences:  A327654 A327655 A327656 * A327658 A327659 A327660

KEYWORD

nonn

AUTHOR

Gus Wiseman, Sep 21 2019

STATUS

approved

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Last modified August 2 02:40 EDT 2021. Contains 346409 sequences. (Running on oeis4.)