

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 crossreferences.
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



