A064133 Number of divisors of 6^n + 1 that are relatively prime to 6^m + 1 for all 0 < m < n.

2, 2, 2, 2, 2, 4, 4, 4, 4, 2, 4, 2, 2, 8, 4, 2, 8, 4, 8, 4, 4, 2, 8, 4, 4, 2, 8, 4, 16, 8, 16, 2, 8, 8, 4, 32, 8, 8, 4, 16, 8, 8, 4, 2, 4, 2, 16, 2, 16, 4, 8, 16, 8, 16, 16, 8, 16, 8, 4, 2, 4, 4, 2, 8, 8, 4, 32, 16, 16, 4, 4, 8, 2, 32, 8, 16, 16, 2, 16, 32, 8

Offset: 0

Author

Robert G. Wilson v, Sep 10 2001

Keywords

• nonn

Links

• Sam Wagstaff, Cunningham Project, Factorizations of 6^n-1, n odd, n<330

Crossrefs

Cf. A064131, A064132, A064134, A064135, A064136, A064137.

Programs

Mathematica

a = {1}; Do[ d = Divisors[ 6^n + 1 ]; l = Length[ d ]; c = 0; k = 1; While[ k < l + 1, If[ Union[ GCD[ a, d[ [ k ] ] ] ] == {1}, c++ ]; k++ ]; Print[ c ]; a = Union[ Flatten[ Append[ a, Transpose[ FactorInteger[ 6^n + 1 ] ][ [ 1 ] ] ] ] ], {n, 0, 66} ]

PARI

a(n) = if (n==0, 2, sumdiv(6^n+1, d, vecsum(vector(n-1, k, gcd(d, 6^k+1) == 1)) == n-1)); \\ Michel Marcus, Jun 24 2018

Extensions

a(67)-a(80) from Giovanni Resta, Jun 26 2018