A064136 Number of divisors of 11^n + 1 that are relatively prime to 11^m + 1 for all 0 < m < n.

2, 6, 2, 2, 2, 2, 4, 2, 4, 2, 2, 16, 4, 8, 8, 4, 4, 8, 2, 16, 4, 2, 4, 16, 16, 4, 2, 4, 16, 8, 2, 16, 8, 16, 16, 48, 8, 4, 4, 8, 4, 8, 4, 4, 16, 8, 16, 16, 4, 16, 8, 8, 2, 16, 16, 32, 16, 8, 16, 16, 4, 8, 4, 16, 4, 8, 4, 64, 32, 32, 4, 8, 8, 32, 64, 8, 16, 16, 64, 16, 128, 8, 8

Offset

0,1

Links

Sean A. Irvine, Table of n, a(n) for n = 0..301

Sam Wagstaff, Cunningham Project, Factorizations of 11^n-1, n<=240

Mathematica

a = {1}; Do[ d = Divisors[ 11^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[ 11^n + 1 ] ][ [ 1 ] ] ] ] ], {n, 0, 55} ]

Prog

(PARI) a(n) = if (n==0, 2, sumdiv(11^n+1, d, vecsum(vector(n-1, k, gcd(d, 11^k+1) == 1)) == n-1)); \\ Michel Marcus, Jun 24 2018

Crossrefs

Cf. A064131, A064132, A064133, A064134, A064135, A064137.

Sequence in context: A332390 A289382 A062539 * A347238 A171898 A378973

Adjacent sequences: A064133 A064134 A064135 * A064137 A064138 A064139

Keyword

nonn,more

Author

Robert G. Wilson v, Sep 10 2001

Extensions

a(1) corrected and more terms from Michel Marcus, Jul 02 2018

a(71)-a(82) from Robert Price, May 26 2019

Status

approved