A064130 Number of divisors of 2^n + 1 that are relatively prime to 2^m + 1 for all 0 < m < n.

2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 4, 2, 2, 2, 4, 2, 4, 4, 8, 2, 2, 4, 4, 2, 4, 4, 8, 4, 4, 4, 8, 2, 2, 4, 4, 2, 4, 2, 16, 4, 4, 2, 8, 8, 4, 4, 4, 4, 4, 4, 4, 8, 2, 2, 16, 2, 4, 8, 4, 4, 4, 4, 4, 4, 4, 4, 16, 2, 8, 8, 16, 2, 4, 8, 16, 32, 4, 2, 16, 2, 8, 8, 8, 8, 2, 4, 8, 4, 2, 16, 8, 4

Offset

0,1

Links

Harry J. Smith, Table of n, a(n) for n = 0..250

Sam Wagstaff, Cunningham Project, Factorizations of 2^n+1, n odd, n<1200

Mathematica

a = {1}; Do[ d = Divisors[ 2^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[ 2^n + 1 ] ][ [ 1 ] ] ] ] ], {n, 0, 100} ]

Prog

(PARI) { allocatemem(932245000); for (n=0, 250, d=divisors(2^n + 1); l=length(d); a=0; for (i=1, l, t=1; for (m=1, n - 1, p=2^m + 1; if (gcd(d[i], p)!=1, t=0; break)); if (t, a++)); write("b064130.txt", n, " ", a) ) } \\ Harry J. Smith, Sep 08 2009

Crossrefs

Sequence in context: A055666 A251139 A195061 * A129139 A032539 A122922

Adjacent sequences: A064127 A064128 A064129 * A064131 A064132 A064133

Keyword

nonn

Author

Robert G. Wilson v, Sep 10 2001

Extensions

Definition corrected from 12^m + 1 to 2^m + 1 by Harry J. Smith, Sep 08 2009

Status

approved