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My solution looks fine in theory, but timeouts in the big number test (rest is fine). Then I created another solution with memoization of results but this one goes out of memory in the the big number test.
It looks I miss some idea from number theory that would allow cutting computation needs dramatically.
Okay problem solved. Thanks @Kecsapo
Nice puzzle! It took me some time to design a solution that would not be harcoded to avoid timeouts.
Like @TBali, I thought I was missing something from number theory in order to quickly identify the set of numbers we had to sum. In the end, I tried something simple and it was enough.