A141214 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.

3, 7, 12, 18, 25, 33, 42, 52, 63, 75, 88, 102, 117, 133, 150, 168, 187, 207, 228, 250, 273, 297, 322, 348, 375, 403, 432, 462, 493, 525, 558, 592, 626, 660, 694

Offset

0,1

Links

Table of n, a(n) for n=0..34.

Formula

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

Example

For degree 2^0, there are 3 polygons of sides 3, 4 & 6.
For degree 2^1, there are 4 polygons of sides 5, 8, 10 & 12.
For degree 2^2 there are 5 (15, 16, 20, 24 & 30).
For n<=31, for degree 2^n, there are n+3 polygons.
For n>= 31 there are 34 polygons.
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.

Crossrefs

The first 32 terms are identical to A055998 and A027379.

Sequence in context: A095115 A310249 A310250 * A027379 A055998 A066379

Adjacent sequences: A141211 A141212 A141213 * A141215 A141216 A141217

Keyword

nonn

Author

Matthew Lehman, Jun 14 2008

Status

approved