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A064131 Number of divisors of 3^n + 1 that are relatively prime to 3^m + 1 for all 0 < m < n. 6

%I

%S 2,3,2,2,2,2,2,2,4,4,2,4,2,2,4,4,2,8,2,4,2,4,4,2,8,4,4,4,4,8,2,4,2,4,

%T 4,2,2,8,4,16,4,4,4,2,8,4,4,8,4,4,8,8,4,4,2,4,8,8,4,4,8,4,8,16,2,2,2,

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

%N Number of divisors of 3^n + 1 that are relatively prime to 3^m + 1 for all 0 < m < n.

%H Sam Wagstaff, Cunningham Project, <a href="https://homes.cerias.purdue.edu/~ssw/cun/">Factorizations of 3^n-1, n odd, n<540</a>

%t a[0]=2; a[n_] := Length@ Select[Divisors[3^n+1], GCD[Times @@ (3^Range[1, n-1] + 1), #] == 1 &]; Array[a, 91, 0] (* _Giovanni Resta_, Jul 02 2018 *)

%o (PARI) a(n) = if (n==0, 2, sumdiv(3^n+1, d, vecsum(vector(n-1, k, gcd(d, 3^k+1) == 1)) == n-1)); \\ _Michel Marcus_, Jun 24 2018

%Y Cf. A064132, A064133, A064134, A064135, A064136, A064137.

%K nonn

%O 0,1

%A _Robert G. Wilson v_, Sep 10 2001

%E a(1) corrected and extended by _Michel Marcus_, Jul 02 2018

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Last modified October 22 09:56 EDT 2019. Contains 328315 sequences. (Running on oeis4.)