This morning, I was reading through most recent American Mathematical Monthly journal, and read two papers; one on summing a particularly slowly converging series, the other on primality in the ring of formal power series. For some reason, this popped a problem into my head; what kind of interesting sequence can we come up with involving primes of integers?
Playing around for a bit, I decided to look at the sum of each integer's prime factors, and make a sequence from the result. After a few modifications, I came up with a couple of interesting theorems, and a few unanswered questions about the results. The work is linked below:
Sum of Prime Factors
I also wonder if similar concepts can be extended to other unique factorization domains. Let me know if you've got any ideas!
Rigor
5 weeks ago
