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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Highly composite number ： ウィキペディア英語版 Highly composite number __NOTOC__ A highly composite number (HCN) is a positive integer with more divisors than any smaller positive integer. The term was coined by Ramanujan (1915). However, Jean-Pierre Kahane has suggested that the concept can be traced back to Plato, who set 5040 as the ideal number of citizens in a city because 5040 has more divisors than smaller numbers.〔. Kahane cites Plato's ''Laws'', 771c.〕 The related concept of largely composite number refers to a positive integer which has at least as many divisors as any smaller positive integer. ==Examples== The initial or smallest 38 highly composite numbers are listed in the table below. The table below shows all the divisors of one of these numbers. The 15,000th highly composite number can be found on Achim Flammenkamp's website. It is the product of 230 primes: : $a\_0^\; a\_1^9\; a\_2^6\; a\_3^4\; a\_4^4\; a\_5^3\; a\_6^3\; a\_7^3\; a\_8^2\; a\_9^2\; a\_^2\; a\_^2\; a\_^2\; a\_^2\; a\_^2\; a\_^2\; a\_^2\; a\_^2\; a\_^\; a\_\; a\_\; a\_\backslash cdots\; a\_,$ where $a\_n$ is the sequence of successive prime numbers, and all omitted terms (''a''22 to ''a''228) are factors with exponent equal to one (i.e. the number is $2^\; \backslash times\; 3^\; \backslash times\; 5^6\; \backslash times\; \backslash cdots\; \backslash times\; 1451$). 〔.〕 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「Highly composite number」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.