A364493 a(n) = A364491(n) * A364492(n).

0, 2, 2, 1, 2, 45, 1, 35, 2, 3, 45, 275, 1, 195, 35, 105, 2, 1377, 3, 2375, 45, 175, 275, 1127, 1, 45, 195, 945, 35, 609, 105, 341, 2, 891, 1377, 875, 3, 13875, 2375, 13377, 45, 9225, 175, 10535, 275, 735, 1127, 5687, 1, 6615, 45, 8925, 195, 5565, 945, 35, 35, 399, 609, 3245, 105, 2013, 341, 819, 2, 47385, 891

Offset: 0

Author

Antti Karttunen, Jul 26 2023

Keywords

• nonn

Links

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

Crossrefs

Cf. A163511, A364255, A364258, A364288, A364491, A364492.

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)))
A364493(n) = { my(u=A163511(n)); (n/gcd(n,u))*(u/gcd(n,u)); };

Python

from math import gcd
from sympy import nextprime
def A364493(n):
    c, p, k = 1, 1, n
    while k:
        c *= (p:=nextprime(p))**(s:=(~k&k-1).bit_length())
        k >>= s+1
    return n*c*p//gcd(c*p,n)**2 # Chai Wah Wu, Jul 26 2023

Formula

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

a(n) = 1 <=> A364258(n) = 0 <=> A364288(n) = 0.