Technical Report Primes, Polynomials and Almost Primes

摘要

A set of almost primes is a set of integers each of which contains no more than a fixed number of prime factors. An integral valued polynomial P(n) which is of degree h and which has k irreducible factors, for example, will generate a sequence of almost primes, the bound being approximately (9h/5 + k log k), [3].nThis paper is accordingly divided into three sections:the main term is developed in the first, the second contains the results we shall need to evaluate the error term, and the third deals with the estimation of the error.