A064129 Number of divisors of 12^n - 1 that are relatively prime to 12^m - 1 for all 0 < m < n.

2, 2, 2, 4, 2, 4, 4, 4, 4, 2, 4, 2, 4, 4, 8, 8, 4, 4, 2, 2, 2, 2, 8, 4, 4, 8, 4, 4, 16, 8, 16, 4, 8, 4, 32, 4, 4, 8, 8, 16, 8, 8, 16, 16, 16, 8, 4, 8, 4, 16, 4, 8, 64, 32, 8, 2, 16, 4, 8, 2, 8, 4, 2, 4, 16, 32, 16, 4, 4, 2, 8, 8, 4, 8, 8, 8, 32, 16, 8, 2, 8

Offset: 1

Author

Robert G. Wilson v, Sep 10 2001

Keywords

• nonn

Links

• Sam Wagstaff, Cunningham Project, Factorizations of 12^n-1, n odd, n<240

Crossrefs

Cf. A063982.

Programs

Mathematica

a = {1}; Do[ d = Divisors[ 12^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[ 12^n - 1 ] ][ [ 1 ] ] ] ] ], {n, 1, 46} ]

PARI

a(n) = sumdiv(12^n-1, d, vecsum(vector(n-1, k, gcd(d, 12^k-1) == 1)) == n-1); \\ Michel Marcus, Jun 23 2018

Extensions

a(47)-a(81) from Jon E. Schoenfield, Jun 23 2018