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Defining A to be the interior angle of a regular polygon, the number of constructible regular polygons such that A is in a field extension <= degree 2^n, starting with n=0. This is also the number of values of x such that phi(x)/2 is a power of 2 <= 2^n (where phi is Euler's phi function), also starting with n=0.
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%I #5 Sep 22 2013 23:15:49

%S 3,7,12,18,25,33,42,52,63,75,88,102,117,133,150,168,187,207,228,250,

%T 273,297,322,348,375,403,432,462,493,525,558,592,626,660,694

%N Defining A to be the interior angle of a regular polygon, the number of constructible regular polygons such that A is in a field extension <= degree 2^n, starting with n=0. This is also the number of values of x such that phi(x)/2 is a power of 2 <= 2^n (where phi is Euler's phi function), also starting with n=0.

%F For 0<n<=31 (n+1)(n+6)/2 For n>=31 34n-462 The formulas are identical when n=31 f(31)=592

%e For degree 2^0, there are 3 polygons of sides 3, 4 & 6.

%e For degree 2^1, there are 4 polygons of sides 5, 8, 10 & 12.

%e For degree 2^2 there are 5 (15, 16, 20, 24 & 30).

%e For n<=31, for degree 2^n, there are n+3 polygons.

%e For n>= 31 there are 34 polygons.

%e Assuming there are only 5 Fermat primes, this is the value of the sum 3+4+5+... up to 31 (and 32) terms, after which each term is 34.

%Y The first 32 terms are identical to A055998 and A027379.

%K nonn

%O 0,1

%A _Matthew Lehman_, Jun 14 2008