2015 regional secondary maymenshing question 10

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barnik
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Joined: Wed Dec 03, 2014 3:37 pm

2015 regional secondary maymenshing question 10

Unread post by barnik » Sun Nov 13, 2016 6:25 pm

In the series $2006,2007,2008,\ldots, 4012$, find the summation of the maximum odd divisor of every number.
Last edited by Phlembac Adib Hasan on Mon Nov 14, 2016 7:22 pm, edited 1 time in total.
Reason: Latexed

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asif e elahi
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Location: Sylhet,Bangladesh

Re: 2015 regional secondary maymenshing question 10

Unread post by asif e elahi » Mon Nov 14, 2016 6:26 pm

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 $2007\leq i<j\leq 4012$.

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