A340148 a(n) = Product_{distinct primes p dividing n} gcd(q-1, A003961(n)-1), where q = A151800(p), the next prime larger than p.

1, 2, 4, 2, 6, 4, 10, 2, 4, 4, 12, 8, 16, 4, 4, 2, 18, 4, 22, 4, 4, 4, 28, 4, 6, 4, 4, 4, 30, 16, 36, 2, 16, 4, 4, 8, 40, 4, 16, 4, 42, 16, 46, 8, 12, 4, 52, 8, 10, 4, 4, 16, 58, 4, 36, 4, 4, 4, 60, 8, 66, 4, 4, 2, 4, 8, 70, 4, 16, 40, 72, 4, 78, 4, 8, 4, 4, 8, 82, 4, 4, 4, 88, 8, 36, 4, 4, 4, 96, 16, 4, 8, 16

Offset: 1

Author

Antti Karttunen, Dec 30 2020

Keywords

• nonn

Comments

Prime shifted analog of A063994.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..8191
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A003961, A003972, A063994, A340147.

Programs

PARI

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A063994(n) = { my(f=factor(n)[,1]); prod(i=1, #f, gcd(f[i]-1, n-1)); };
A340148(n) = A063994(A003961(n));

PARI

A340148(n) = { my(f=factor(n)[,1], u=A003961(n)); prod(i=1, #f, gcd(nextprime(1+f[i])-1, u-1)); };

PARI

A340148(n) = { my(u=A003961(n), f=factor(u)[,1]); prod(i=1, #f, gcd(f[i]-1, u-1)); };

Formula

a(n) = A063994(A003961(n)).

a(n) = A003972(n) / A340147(n).