On wide-output sieves

Abstract

We describe and compare several novel sieve-like methods. They assign values of several functions (i.e., the prime omega functions ω and Ω and the divisor function d) to each natural number in the considered range of integer numbers. We prove that in some cases the algorithms presented have a relatively small computational complexity. A more detailed output is indeed obtained with respect to the original Sieve of Eratosthenes.