A355815 a(n) = gcd(A276086(n), A277791(n)), where A276086 is primorial base exp-function and A277791 is the denominator of sum of reciprocals of proper divisors of n.

1, 1, 1, 1, 1, 1, 1, 1, 3, 5, 1, 1, 1, 1, 15, 1, 1, 1, 1, 5, 3, 1, 1, 1, 5, 1, 3, 1, 1, 1, 1, 1, 3, 1, 7, 1, 1, 1, 3, 5, 1, 7, 1, 1, 15, 1, 1, 1, 7, 25, 3, 1, 1, 1, 5, 1, 3, 1, 1, 1, 1, 1, 21, 1, 1, 1, 1, 1, 3, 35, 1, 1, 1, 1, 25, 1, 7, 1, 1, 1, 3, 1, 1, 7, 5, 1, 3, 1, 1, 1, 7, 1, 3, 1, 1, 1, 1, 49, 3, 5, 1, 1, 1, 1, 105

Offset: 1

Author

Antti Karttunen, Jul 18 2022

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..11550
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
• Index entries for sequences related to primorial base

Crossrefs

Sequence contains only terms of A048103.

Cf. A276086, A277791.

Cf. also A327858, A355003.

Programs

PARI

A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A277791(n) = denominator((sigma(n)-1)/n); \\ From A277791
A355815(n) = gcd(A276086(n), A277791(n));

Python

from math import gcd
from sympy import nextprime, divisor_sigma
def A355815(n):
    m, p, c = 1, 2, n
    while c:
        c, a = divmod(c,p)
        m *= p**a
        p = nextprime(p)
    return gcd(m,n//gcd(n, divisor_sigma(n)-1)) # Chai Wah Wu, Jul 18 2022

Formula

a(n) = gcd(A276086(n), A277791(n)).