A364492 a(n) = A163511(n) / gcd(n, A163511(n)).

1, 2, 2, 1, 2, 9, 1, 5, 2, 3, 9, 25, 1, 15, 5, 7, 2, 81, 3, 125, 9, 25, 25, 49, 1, 9, 15, 35, 5, 21, 7, 11, 2, 81, 81, 125, 3, 375, 125, 343, 9, 225, 25, 245, 25, 49, 49, 121, 1, 135, 9, 175, 15, 105, 35, 7, 5, 21, 21, 55, 7, 33, 11, 13, 2, 729, 81, 3125, 81, 625, 125, 2401, 3, 1125, 375, 343, 125, 147, 343, 1331

Offset: 0

Author

Antti Karttunen, Jul 26 2023

Keywords

• nonn
• frac

Comments

Denominator of n / A163511(n).

Links

• Antti Karttunen, Table of n, a(n) for n = 0..16383

Crossrefs

Cf. A163511, A364255, A364491 (numerators), A364493, A364496 (positions of 1's).

Programs

PARI

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
A054429(n) = ((3<<#binary(n\2))-n-1);
A163511(n) = if(!n,1,A005940(1+A054429(n)))
A364492(n) = { my(u=A163511(n)); (u/gcd(n, u)); };

Python

from math import gcd
from sympy import nextprime
def A364492(n):
    c, p, k = 1, 1, n
    while k:
        c *= (p:=nextprime(p))**(s:=(~k&k-1).bit_length())
        k >>= s+1
    return c*p//gcd(c*p,n) # Chai Wah Wu, Jul 26 2023

Formula

a(n) = A163511(n) / A364255(n) = A163511(n) / gcd(n, A163511(n)).