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

%I #13 Jan 18 2019 13:56:37

%S 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,

%T 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,

%U 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

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

%H Harry J. Smith, <a href="/A064130/b064130.txt">Table of n, a(n) for n = 0..250</a>

%H Sam Wagstaff, Cunningham Project, <a href="https://homes.cerias.purdue.edu/~ssw/cun/">Factorizations of 2^n+1, n odd, n<1200</a>

%t 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} ]

%o (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

%K nonn

%O 0,1

%A _Robert G. Wilson v_, Sep 10 2001

%E Definition corrected from 12^m + 1 to 2^m + 1 by _Harry J. Smith_, Sep 08 2009