Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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