Asymptotically Exact Heuristics for Prime Divisors of the Sequence {a/k + b/k} §k
| Authors | |
|---|---|
| Publication date | 2006 |
| Journal | Journal of Integer Sequences |
| Volume | Issue number | 9 |
| Pages (from-to) | article 06.2.8 |
| Organisations |
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| Abstract | Let N a,b (x) count the number of primes p = x with p dividing a k + b k for some k = 1. It is known that N a,b (x) ~ c(a,b)x/log x for some rational number c(a,b) that depends in a rather intricate way on a and b. A simple heuristic formula for N a,b (x) is proposed and it is proved that it is asymptotically exact, i.e. has the same asymptotic behaviour as N a,b (x). Connections with Ramanujan sums and character sums are discussed. |
| Document type | Article |
| Note | electronisch |
| Published at | http://www.cs.uwaterloo.ca/journals/JIS/VOL9/Moree/moree45.pdf |
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