Editing Bell number (section)

===Factorizations===
If a number <math>N</math> is a [[squarefree]] positive [[integer]], meaning that it is the product of some number <math>n</math> of distinct [[prime number]]s, then <math>B_n</math> gives the number of different [[multiplicative partition]]s of <math>N</math>. These are [[factorization]]s of <math>N</math> into numbers greater than one, treating two factorizations as the same if they have the same factors in a different order.<ref>{{harvnb|Williams|1945}} credits this observation to Silvio Minetola's ''Principii di Analisi Combinatoria'' (1909).</ref> For instance, 30 is the product of the three primes 2, 3, and&nbsp;5, and has <math>B_3</math> = 5 factorizations:
:<math>30 = 2\times 15=3\times 10=5\times 6=2\times 3\times 5</math>