A331283 a(n) = gcd(n, A329605(n)), where A329605(n) gives the number of divisors of primorial inflation of n, A108951(n).

1, 2, 1, 1, 1, 6, 1, 4, 9, 2, 1, 4, 1, 2, 3, 1, 1, 6, 1, 4, 3, 2, 1, 2, 1, 2, 1, 4, 1, 6, 1, 2, 3, 2, 1, 3, 1, 2, 3, 20, 1, 6, 1, 4, 1, 2, 1, 12, 1, 2, 3, 4, 1, 2, 1, 8, 3, 2, 1, 30, 1, 2, 1, 1, 1, 6, 1, 4, 3, 2, 1, 18, 1, 2, 3, 4, 1, 6, 1, 8, 1, 2, 1, 12, 1, 2, 3, 8, 1, 10, 1, 4, 3, 2, 1, 2, 1, 2, 1, 5, 1, 6, 1, 8, 3

Offset: 1

Author

Antti Karttunen, Jan 14 2020

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..11025
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to primorial numbers

Crossrefs

Cf. A000142, A002110, A034386, A108951, A329605.

Cf. also A009191, A329612.

Programs

PARI

A331283(n) = if(1==n,1,my(f=factor(n),e=1,m=1); forstep(i=#f~,1,-1, e += f[i,2]; m *= e^(primepi(f[i,1])-if(1==i,0,primepi(f[i-1,1])))); gcd(n,m));

Formula

a(n) = gcd(n, A329605(n)).

a(A002110(n)) = gcd(A002110(n), A000142(1+n)) = A034386(1+n), for n >= 0.