Quantum.Mechanic

Yes, thanks very much. I got lost trying to do this myself, but "it's obvious in hindsight", as they say.

I must be thick today, I can't follow the given solution. Can someone paste a little bit more hand holding? Like the first 5 values in the sequence?

Since the integer requirement, there haven't been any replies, so I'll go with an obvious, and not-likely-to-be-optimal one.

OK, I thought that would be a good little puzzle program to write. I'm sure there's an easier way to figure this on paper though, waiting for y'all to clue me in. The first few elements led me to the following:

Are we assuming a mammalian birth process? Then splitting is in utero, and age origin is time of birth. When in Thailand...

Just for fun, I programmed up a little script. Using a suitable underlying GMP library for Euler's totient function, it checked up to 10 million in 13 seconds, with a result of 60.793% distinct pairs relatively prime.

Maximum sum, or highest numbered side?

I saw this puzzle in the same Peter Winkler book I mentioned elsewhere.

Testing a few targets other than 99,

I wrote a program to check.