Problem 355
Maximal coprime subset

Define Co(n) to be the maximal possible sum of a set of mutually co-prime elements from {1, 2, ..., n}.
For example Co(10) is 30 and hits that maximum on the subset {1, 5, 7, 8, 9}.

You are given that Co(30) = 193 and Co(100) = 1356.

Find Co(200000).

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http://projecteuler.net/problem=355