ON THE LARGEST PRIME FACTOR OF THE PARTITION FUNCTION OF n

@inproceedings{Cilleruelo2012ONTL,
  title={ON THE LARGEST PRIME FACTOR OF THE PARTITION FUNCTION OF n},
  author={Javier Cilleruelo},
  year={2012}
}
Let p(n) be the function that counts the number of partitions of n. For a positive integer m, let P (m) be the largest prime factor of m. Here, we show that P (p(n)) tends to infinity when n tends to infinity through some set of asymptotic density 1. In fact, we show that the inequality P (p(n)) > log log n holds for almost all positive integers n. This… CONTINUE READING