A364491 a(n) = n / gcd(n, A163511(n)).

0, 1, 1, 1, 1, 5, 1, 7, 1, 1, 5, 11, 1, 13, 7, 15, 1, 17, 1, 19, 5, 7, 11, 23, 1, 5, 13, 27, 7, 29, 15, 31, 1, 11, 17, 7, 1, 37, 19, 39, 5, 41, 7, 43, 11, 15, 23, 47, 1, 49, 5, 51, 13, 53, 27, 5, 7, 19, 29, 59, 15, 61, 31, 63, 1, 65, 11, 67, 17, 23, 7, 71, 1, 73, 37, 15, 19, 11, 39, 79, 5, 3, 41, 83, 7, 17, 43, 87

Offset: 0

Author

Antti Karttunen, Jul 26 2023

Keywords

• nonn
• frac

Comments

Numerator of n / A163511(n).

Links

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

Crossrefs

Cf. A163511, A364255, A364492 (denominators), A364493, A364494 (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); \\ From A054429
A163511(n) = if(!n,1,A005940(1+A054429(n)))
A364491(n) = (n/gcd(n, A163511(n)));

Python

from math import gcd
from sympy import nextprime
def A364491(n):
    c, p, k = 1, 1, n
    while k:
        c *= (p:=nextprime(p))**(s:=(~k&k-1).bit_length())
        k >>= s+1
    return n//gcd(c*p,n) # Chai Wah Wu, Jul 26 2023

Formula

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