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正规数 (整数)

一个400以内正规数其约数关系的哈斯图,其纵向为对数尺度[1]

正规数Regular numbers)是指可以整除60的乘幂的整数,也就是60乘幂的约数,例如602 = 3600 = 48 × 75,48和75都可以整除60的平方,也都是正规数。

在许多数学及应用的领域会用到60乘幂的约数,在不同的领域中其名称也有所不同。

  • 数论中,60乘幂的约数也称为5-光滑数,因为其素因数只有2,3或是5,这是k-光滑数中的一个特例,k-光滑数是指其素因数都小于等于k的整数。
  • 巴比伦数学中,60乘幂的约数称为正规数或是60正规数,因为巴比伦数学是使用六十进制,因此这类数字格外的重要。
  • 计算机科学,60乘幂的约数称为汉明数Hamming numbers),得名自数学家理查德·卫斯里·汉明,他提出一个用电脑依序找出60乘幂的约数的算法

注释

  1. ^ Inspired by similar diagrams by Erkki Kurenniemi in "Chords, scales, and divisor lattices"页面存档备份,存于互联网档案馆).

参考资料

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  • Asmussen, Robert, Periodicity of sinusoidal frequencies as a basis for the analysis of Baroque and Classical harmony: a computer based study (PDF), Ph.D. thesis, Univ. of Leeds, 2001 [2012-12-27], (原始内容 (PDF)存档于2016-04-24) .
  • Barton, George A., On the Babylonian origin of Plato's nuptial number, Journal of the American Oriental Society (American Oriental Society), 1908, 29: 210–219, JSTOR 592627, doi:10.2307/592627 .
  • Bruins, E. M., La construction de la grande table le valeurs réciproques AO 6456, Finet, André (编), Actes de la XVIIe Rencontre Assyriologique Internationale, Comité belge de recherches en Mésopotamie: 99–115, 1970 .
  • Conway, John H.; Guy, Richard K., The Book of Numbers, Copernicus: 172–176, 1996, ISBN 0-387-97993-X .
  • Dijkstra, Edsger W., Hamming's exercise in SASL (PDF), 1981 [2012-12-27], Report EWD792. Originally a privately-circulated handwitten note, (原始内容存档 (PDF)于2019-04-04) .
  • Eppstein, David, The range-restricted Hamming problem, 2007, (原始内容存档于2011-07-21) .
  • Gingerich, Owen, Eleven-digit regular sexagesimals and their reciprocals, Transactions of the American Philosophical Society (American Philosophical Society), 1965, 55 (8): 3–38, JSTOR 1006080, doi:10.2307/1006080 .
  • Habens, Rev. W. J., On the musical scale, Proceedings of the Musical Association (Royal Musical Association), 1889, 16: 16th Session, p. 1, JSTOR 765355 .
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正规数 (整数)
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