A327168 Number of common divisors of n and A276086(n), with a(0) = 1.

1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 4, 1, 1, 1, 1, 2, 2, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 2, 1, 2, 1, 1, 4, 1, 1, 1, 2, 3, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 2, 4, 1, 1, 1, 1, 6, 1, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 3, 2, 2, 1, 1, 1, 1, 8

Offset: 0

Author

Antti Karttunen, Sep 19 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..16383
• Antti Karttunen, Data supplement: n, a(n) computed for n = 0..65537
• Index entries for sequences related to primorial base

Crossrefs

Cf. A000005, A001222, A276086, A324198, A327167.

Cf. also A323878.

Programs

PARI

A276086(n) = { my(i=0,m=1,pr=1,nextpr); while((n>0),i=i+1; nextpr = prime(i)*pr; if((n%nextpr),m*=(prime(i)^((n%nextpr)/pr));n-=(n%nextpr));pr=nextpr); m; };
A327168(n) = numdiv(gcd(n,A276086(n)));

Formula

a(n) = A000005(A324198(n)).

a(n) = 1+A001222(A327167(n)) for n >= 1.