|
%I #12 Jan 18 2019 13:56:37
%S 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,
%T 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,
%U 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
%N Number of divisors of 3^n - 1 that are relatively prime to 3^m - 1 for all 0 < m < n.
%H Harry J. Smith, <a href="/A064122/b064122.txt">Table of n, a(n) for n = 1..167</a>
%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 = {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} ]
%o (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
%Y Cf. A063982.
%K nonn
%O 1,1
%A _Robert G. Wilson v_, Sep 10 2001
|
