A356153 Denominator of n / the smallest positive k such that n divides k*A276086(k), where A276086 is primorial base exp-function.

1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 4, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 5, 1, 3, 1, 1, 1, 1, 2

Offset: 1

Author

Antti Karttunen, Jul 28 2022

Keywords

• nonn
• frac

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences related to primorial base

Crossrefs

Cf. A276086, A324580, A355944, A355945, A356151, A356152 (numerators), A356154 (Dirichlet inverse).

Programs

PARI

A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A356153(n) = for(k=1, oo, if((k*A276086(k))%n==0, return(k/gcd(n,k))));

Formula

a(n) = A355944(n) / A356151(n) = A355944(n) / gcd(n, A355944(n)).