Fun Facts about 2010 and 2011 #2

From : November 6, 2010

http://benvitale-funwithnum3ers.blogspot.com/2010/11/fun-facts-about-2010-and-2011.html

2011 is a Loeschian number : 2011 = 10^2 + 10*39 + 39^2

http://oeis.org/A003136

2007 was a Loeschian number and the next one will be 2017.

Using the equation x^2 + xy + y^2 find the other Loeschian years of this century.

Notice that:

2011^2 = 4 044 121

1102^2 = 1 214 404

Quite remarkable!

The factors of 4044121 are: 1 2011 4044121
The prime factors are: 2011 * 2011

The factors of 1214404 are: 1 2 4 19 29 38 58 76 116 361 551 722 841 1102 1444 1682 2204 3364 10469 15979 20938 31958 41876 63916 303601 607202 1214404

The prime factors are: 2 * 2 * 19 * 19 * 29 * 29


2011 = 44^2 + 8^2 + 3^2 + 1^2 + 1^2

2011 = 12^3 + 6^3 + 4^3 + 1^3 + 1^3 + 1^3

2011 = (7! - 6!)/2 - (5 !) - (4 !) - (3 !) + (1 !)