On the maximal order of numbers in the "factorisatio numerorum" problem
| dc.creator | Klazar, Martin | |
| dc.creator | Luca, Florian | |
| dc.date | 2005-05-17 | |
| dc.date | 2006-07-07 | |
| dc.date.accessioned | 2026-07-07T06:39:58Z | |
| dc.date.available | 2026-07-07T06:39:58Z | |
| dc.description | Let m(n) be the number of ordered factorizations of n in factors larger than 1. We prove that for every eps>0 n^{rho} m(n) < exp[(log n)^{1/rho}/(loglog n)^{1+eps}] holds for all integers n>n_0, while, for a constant c>0, n^{rho} m(n) > exp[c(log n)^{1/ρ}/(loglog n)^{1/rho}] holds for infinitely many positive integers n, where rho=1.72864... is the real solution to zeta(rho)=2. We investigate also arithmetic properties of m(n) and the number of distinct values of m(n). | |
| dc.description | We have rewritten the paper and improved considerably the lower bound. Thus now we know that the max. order of m(n) is n^{rho}/(exp((log n)^{1/rho+o(1)})). Submitted to JNT | |
| dc.identifier | https://arxiv.org/abs/math/0505352 | |
| dc.identifier | http://arxiv.org/abs/math/0505352 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/101279 | |
| dc.subject | Number Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 11N56; 05A17 | |
| dc.title | On the maximal order of numbers in the "factorisatio numerorum" problem | |
| dc.type | text |