|
%I #8 Jan 18 2019 13:56:37
%S 4,1,2,3,2,2,4,2,4,4,4,4,2,4,4,4,4,2,4,4,2,4,8,8,4,4,16,2,8,2,8,4,8,2,
%T 4,2,8,4,8,4,8,4,4,8,4,2,4,2,16,2,16,4,8,2,2,16,8,2,16,4,16,8,2,8,32,
%U 4,16,8,8,16,4,8,32,4,4,2,8,8,4,8,16,16,128,2,8
%N Number of divisors of 7^n - 1 that are relatively prime to 7^m - 1 for all 0 < m < n.
%H Sam Wagstaff, Cunningham Project, <a href="https://homes.cerias.purdue.edu/~ssw/cun/">Factorizations of 7^n-1, n odd, n<300</a>
%t a = {1}; Do[ d = Divisors[ 7^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[ 7^n - 1 ] ][ [ 1 ] ] ] ] ], {n, 1, 70} ]
%o (PARI) a(n) = sumdiv(7^n-1, d, vecsum(vector(n-1, k, gcd(d, 7^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(71)-a(85) from _Giovanni Resta_, Jun 26 2018
|
