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%I #14 Jan 18 2019 13:56:37
%S 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,
%T 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,
%U 8,8,4,32,16,16,4,4,8,2,32,8,16,16,2,16,32,8
%N Number of divisors of 6^n + 1 that are relatively prime to 6^m + 1 for all 0 < m < n.
%H Sam Wagstaff, Cunningham Project, <a href="https://homes.cerias.purdue.edu/~ssw/cun/">Factorizations of 6^n-1, n odd, n<330</a>
%t 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} ]
%o (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
%Y Cf. A064131, A064132, A064134, A064135, A064136, A064137.
%K nonn
%O 0,1
%A _Robert G. Wilson v_, Sep 10 2001
%E a(67)-a(80) from _Giovanni Resta_, Jun 26 2018
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