A355001 Smallest common prime factor of A003961(n) and A276086(n), or 1 if they are coprime, where A003961 is fully multiplicative with a(p) = nextprime(p), and A276086 is primorial base exp-function.

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

Offset: 1

Author

Antti Karttunen, Jul 13 2022

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100000
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to primorial base

Crossrefs

Cf. A003961, A020639, A276086, A284723 (even bisection), A355442, A355820, A355821 (positions of 1's).

Programs

PARI

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A020639(n) = if(1==n,n,vecmin(factor(n)[, 1]));
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));
A355001(n) = A020639(A355442(n));

Formula

a(n) = A020639(A355442(n)) = A020639(gcd(A003961(n), A276086(n))).