cp's OEIS Frontend

A141213 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 = 2^n (where phi is Euler's phi function), also starting with n=0.

%I A141213 #7 Nov 13 2018 00:37:07
%S A141213 3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,
%T A141213 28,29,30,31,32,33,34,34,34
%N A141213 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 = 2^n (where phi is Euler's phi function), also starting with n=0.
%F A141213 For n<=31, f(n)=n+3; for n>=31, f(n)=34.
%e A141213 For degree 2^0, there are 3 polygons with 3, 4 & 6 sides.
%e A141213 For degree 2^1, there are 4 polygons with 5, 8, 10 & 12 sides.
%e A141213 For degree 2^2 there are 5 polygons with 15, 16, 20, 24 & 30 sides.
%e A141213 For n<=31, for degree 2^n, there are n+3 polygons.
%e A141213 For n>= 31 there are 34 polygons.
%e A141213 Assuming there are only five Fermat primes, the sequence will continue repeating 34 forever.
%Y A141213 Cf. A141214.
%K A141213 nonn
%O A141213 0,1
%A A141213 _Matthew Lehman_, Jun 14 2008