A355456 Greatest common divisor of sigma(n), A003961(n), and A276086(n).

1, 3, 1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 3, 1, 5, 1, 3, 5, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 3, 1, 9, 1, 1, 1, 3, 1, 3, 1, 1, 1, 3, 1, 1, 1, 5, 1, 3, 5, 3, 1, 7, 1, 3, 1, 1, 7, 1, 1, 3, 1, 3, 1, 5, 1, 3, 1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 3, 5, 9, 1, 1, 1, 3, 1, 3, 1, 1, 1, 3, 1, 7, 1, 1, 1, 3, 1

Offset: 1

Author

Antti Karttunen, Jul 13 2022

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to primorial base
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A003961, A276086, A324644, A342671, A355442, A355002 (terms k such that a(k) shares a prime factor with k).

Cf. also A323653, A351459.

Programs

PARI

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A355442(n) = gcd(A003961(n), A276086(n));
A355456(n) = gcd(sigma(n), A355442(n));

Formula

a(n) = gcd(A000203(n), A355442(n)).

a(n) = gcd(A324644(n), A342671(n)) = gcd(A276086(n), A342671(n)) = gcd(A003961(n), A324644(n)).