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Wednesday, June 4, 2008

Sum of Prime Factors

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!


vlorbik said...

how do you create those pdf's?
i've got all manner of old TeX
files lying around here that
i'd love to make public ...

fashionablemathematician said...

Vlorbik, I'm running the latest versions of MikTex and Winedt. My TeX editor, WinEdt, is compatible with most TeX formattings, and can export to a number of formats, including PDF. MikTex is free, Winedt is $30 to register for a lifetime, and I've found it to be worth the money.


catsynth said...

Cool. I'm including your article in this weekend's Carnival of Mathematics. I'm always interested to see work with prime numbers.