A064129 - OEIS

%I #10 Jan 18 2019 13:56:37

%S 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,

%T 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,

%U 4,16,32,16,4,4,2,8,8,4,8,8,8,32,16,8,2,8

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

%H Sam Wagstaff, Cunningham Project, <a href="https://homes.cerias.purdue.edu/~ssw/cun/">Factorizations of 12^n-1, n odd, n<240</a>

%t 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} ]

%o (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

%Y Cf. A063982.

%K nonn

%O 1,1

%A _Robert G. Wilson v_, Sep 10 2001

%E a(47)-a(81) from _Jon E. Schoenfield_, Jun 23 2018