Divisor is fun

Compute the sum of the greatest odd divisor of each of the numbers 2006, 2007, ... , 4012.


Problem Source: 104 Number Theory Problems by Titu Andreescu, Dorin Andrica, Zuming Feng.
( 2006 ) 2 (2006)^2 1003 + ( 2006 ) 2 1003 + (2006)^2

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