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In number theory, a multiplicative partition or unordered factorization of an integer ''n'' that is greater than 1 is a way of writing ''n'' as a product of integers greater than 1, treating two products as equivalent if they differ only in the ordering of the factors. The number ''n'' is itself considered one of these products. Multiplicative partitions closely parallel the study of multipartite partitions, discussed in , which are additive partitions of finite sequences of positive integers, with the addition made pointwise. Although the study of multiplicative partitions has been ongoing since at least 1923, the name "multiplicative partition" appears to have been introduced by . The Latin name "factorisatio numerorum" had been used previously. MathWorld uses the term unordered factorization. ==Examples== *The number 20 has four multiplicative partitions: 2 × 2 × 5, 2 × 10, 4 × 5, and 20. *3 × 3 × 3 × 3, 3 × 3 × 9, 3 × 27, 9 × 9, and 81 are the five multiplicative partitions of 81 = 34. Because it is the fourth power of a prime, 81 has the same number (five) of multiplicative partitions as 4 does of additive partitions. *The number 30 has five multiplicative partitions: 2 × 3 × 5 = 2 × 15 = 6 × 5 = 3 × 10 = 30. *In general, the number of multiplicative partitions of a squarefree number with i prime factors is the ith Bell number, Bi. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「multiplicative partition」の詳細全文を読む スポンサード リンク
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