A064122 Number of divisors of 3^n - 1 that are relatively prime to 3^m - 1 for all 0 < m < n.

2, 1, 2, 2, 3, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 4, 4, 4, 4, 2, 2, 4, 4, 2, 4, 2, 8, 4, 8, 4, 8, 2, 2, 8, 4, 2, 4, 4, 8, 2, 8, 4, 4, 4, 8, 2, 16, 8, 32, 4, 4, 4, 8, 4, 4, 4, 8, 8, 4, 2, 4, 4, 2, 2, 8, 4, 8, 4, 4, 2, 2, 2, 16, 8, 8, 4, 8, 16, 8, 4, 8, 4, 16, 4, 4, 2, 8, 8, 8, 4, 4, 4, 4, 8, 4, 4, 8, 4, 4, 8

Offset: 1

Author

Robert G. Wilson v, Sep 10 2001

Keywords

• nonn

Links

• Harry J. Smith, Table of n, a(n) for n = 1..167
• Sam Wagstaff, Cunningham Project, Factorizations of 3^n-1, n odd, n<540

Crossrefs

Cf. A063982.

Programs

Mathematica

a = {1}; Do[ d = Divisors[ 3^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[ 3^n - 1 ] ][ [ 1 ] ] ] ] ], {n, 1, 100} ]

PARI

{ allocatemem(932245000); for (n=1, 167, d=divisors(3^n - 1); l=length(d); a=0; for (i=1, l, t=1; for (m=1, n - 1, p=3^m - 1; if (gcd(d[i], p)!=1, t=0; break)); if (t, a++)); write("b064122.txt", n, " ", a) ) } \\ Harry J. Smith, Sep 08 2009