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sums with greatest odd divisor of n

Source: Flanders Math Olympiad 2018 p3

December 24, 2022
number theoryDivisorsdivisorSum

Problem Statement

Write down f(n)f(n) for the greatest odd divisor of n∈N0n \in N_0. (a) Determine f(n+1)+f(n+2)+...+f(2n)f (n + 1) + f (n + 2) + ... + f(2n). (b) Determine f(1)+f(2)+f(3)+...+f(2n)f(1) + f(2) + f(3) + ... + f(2n).
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