A3 = {3, 5}, as 12 contains the factor 4 = 22, which is not in A3. Note the set A does not have to be a set of prime factors, but it is typically a proper subset of the primes as seen in the factor base of Dixon's factorization method and the quadratic sieve. Likewise, it is what the general number field sieve uses to build its notion of smoothness, under the homomorphism . See also Highly composite number Rough number Round number Størmer's theorem Unusual number Notes and references Bibliography G. Tenenbaum, Introduction to analytic and probabilistic number theory, (AMS, 2015) A. Granville, Smooth numbers: Computational number theory and beyond, Proc. of MSRI workshop, 2008 External links The On-Line Encyclopedia of Integer Sequences (OEIS) lists B-smooth numbers for small Bs: 2-smooth numbers: A000079 (2i) 3-smooth numbers: A003586 (2i3j) 5-smooth numbers: A051037 (2i3j5k) 7-smooth numbers: A002473 (2i3j5k7l) 11-smooth numbers: A051038 (etc...) 13-smooth numbers: A080197 17-smooth numbers: A080681 19-smooth numbers: A080682 23-smooth numbers: A080683 Analytic number theory Integer sequences