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A064133 Number of divisors of 6^n + 1 that are relatively prime to 6^m + 1 for all 0 < m < n. 6
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, 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, 8, 8, 4, 32, 16, 16, 4, 4, 8, 2, 32, 8, 16, 16, 2, 16, 32, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..80.

Sam Wagstaff, Cunningham Project, Factorizations of 6^n-1, n odd, n<330

MATHEMATICA

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} ]

PROG

(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

CROSSREFS

Cf. A064131, A064132, A064134, A064135, A064136, A064137.

Sequence in context: A319820 A319799 A294078 * A295101 A160675 A105674

Adjacent sequences:  A064130 A064131 A064132 * A064134 A064135 A064136

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Sep 10 2001

EXTENSIONS

a(67)-a(80) from Giovanni Resta, Jun 26 2018

STATUS

approved

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Last modified September 18 05:32 EDT 2019. Contains 327165 sequences. (Running on oeis4.)