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

1,9

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

Formula

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

Prog

(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

Crossrefs

Sequence contains only terms of A048103.

Cf. A276086, A277791.

Cf. also A327858, A355003.

Sequence in context: A016452 A346095 A091717 * A154512 A030588 A307860

Adjacent sequences: A355812 A355813 A355814 * A355816 A355817 A355818

Keyword

nonn

Author

Antti Karttunen, Jul 18 2022

Status

approved