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Sum of greatest odd divisors equal n^2

Source: ToT 2003-JO-3, SO-1

June 18, 2011
number theory proposednumber theory

Problem Statement

For any integer n+1,…,2nn+1,\ldots, 2n (nn is a natural number) consider its greatest odd divisor. Prove that the sum of all these divisors equals n2.n^2.
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