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2015 regional secondary maymenshing question 10

Posted: Sun Nov 13, 2016 6:25 pm
by barnik
In the series $2006,2007,2008,\ldots, 4012$, find the summation of the maximum odd divisor of every number.

Re: 2015 regional secondary maymenshing question 10

Posted: Mon Nov 14, 2016 6:26 pm
by asif e elahi
Hint
Let $f(i)$ denote the largest odd divisor of $i$ for all $i \in \mathbb{N}$. Prove that $f(i)\neq f(j)$ for $2007\leq i<j\leq 4012$.