|
Regular numbers are numbers that evenly divide powers of 60 (or, equivalently powers of 30). As an example, 602 = 3600 = 48 × 75, so both 48 and 75 are divisors of a power of 60. Thus, they are ''regular numbers''. Equivalently, they are the numbers whose only prime divisors are 2, 3, and 5. The numbers that evenly divide the powers of 60 arise in several areas of mathematics and its applications, and have different names coming from these different areas of study. * In number theory, these numbers are called 5-smooth, because they can be characterized as having only 2, 3, or 5 as prime factors. This is a specific case of the more general ''k''-smooth numbers, i.e., a set of numbers that have no prime factor greater than ''k''. * In the study of Babylonian mathematics, the divisors of powers of 60 are called regular numbers or regular sexagesimal numbers, and are of great importance due to the sexagesimal number system used by the Babylonians. * In music theory, regular numbers occur in the ratios of tones in five-limit just intonation. * In computer science, regular numbers are often called Hamming numbers, after Richard Hamming, who proposed the problem of finding computer algorithms for generating these numbers in order. == Number theory == Formally, a regular number is an integer of the form 2''i''·3''j''·5''k'', for nonnegative integers ''i'', ''j'', and ''k''. Such a number is a divisor of Even more precisely, using big O notation, the number of regular numbers up to ''N'' is : and it has been conjectured that the error term of this approximation is actually . A similar formula for the number of 3-smooth numbers up to ''N'' is given by Srinivasa Ramanujan in his first letter to G. H. Hardy.〔.〕 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「regular number」の詳細全文を読む スポンサード リンク
|