# 正规数 (整数)

• 數論中，60乘幂的因數也稱為5-光滑數，因為其質因數只有2,3或是5，這是k-光滑數中的一個特例，k-光滑數是指其質因數都小於等於k的整數。
• 巴比伦数学中，60乘幂的因數稱為正规数或是60正规数，因為巴比伦数学是使用六十進制，因此這類數字格外的重要。
• 計算機科學，60乘幂的因數稱為漢明數Hamming numbers），得名自數學家理查德·衛斯里·漢明，他提出一個用電腦依序找出60乘幂的因數的演算法

## Notes

1. ^ Inspired by similar diagrams by Erkki Kurenniemi in "Chords, scales, and divisor lattices".

## 参考资料

• Aaboe, Asger, Some Seleucid mathematical tables (extended reciprocals and squares of regular numbers), Journal of Cuneiform Studies. The American Schools of Oriental Research. 1965, 19 (3): 79–86, doi:10.2307/1359089 .
• Asmussen, Robert, Periodicity of sinusoidal frequencies as a basis for the analysis of Baroque and Classical harmony: a computer based study, Ph.D. thesis, Univ. of Leeds. 2001 .
• 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, doi:10.2307/592627 .
• Bruins, E. M., La construction de la grande table le valeurs réciproques AO 6456//Finet, André, Actes de la XVIIe Rencontre Assyriologique Internationale, Comité belge de recherches en Mésopotamie. 1970:  99–115 .
• Conway, John H.; Guy, Richard K., The Book of Numbers, Copernicus. 1996:  172–176, ISBN 0-387-97993-X .
• Dijkstra, Edsger W., Hamming's exercise in SASL. 1981, Report EWD792. Originally a privately-circulated handwitten note .
•  .
• Gingerich, Owen, Eleven-digit regular sexagesimals and their reciprocals, Transactions of the American Philosophical Society. American Philosophical Society. 1965, 55 (8): 3–38, 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 .
• Halsey, G. D.; Hewitt, Edwin, More on the superparticular ratios in music, American Mathematical Monthly. Mathematical Association of America. 1972, 79 (10): 1096–1100, doi:10.2307/2317424 .
• Hemmendinger, David, The "Hamming problem" in Prolog, ACM SIGPLAN Notices. 1988, 23 (4): 81–86, doi:10.1145/44326.44335 .
• Heninger, Nadia; Rains, E. M.; Sloane, N. J. A.. On the integrality of nth roots of generating functions. arXiv:math.NT/0509316. 2005. .
• Honingh, Aline; Bod, Rens, Convexity and the well-formedness of musical objects, Journal of New Music Research. 2005, 34 (3): 293–303, doi:10.1080/09298210500280612 .
• Knuth, D. E., Ancient Babylonian algorithms, Communications of the ACM. 1972, 15 (7): 671–677, doi:10.1145/361454.361514 . Errata in CACM 19(2), 1976. Reprinted with a brief addendum in Selected Papers on Computer Science, CSLI Lecture Notes 59, Cambridge Univ. Press, 1996, pp. 185–203.
• Longuet-Higgins, H. C., Letter to a musical friend, Music Review. 1962 (August): 244–248 .
• McClain, Ernest G.; Plato,, Musical "Marriages" in Plato's "Republic", Journal of Music Theory. Duke University Press. 1974, 18 (2): 242–272, doi:10.2307/843638 .
• Sachs, A. J., Babylonian mathematical texts. I. Reciprocals of regular sexagesimal numbers, Journal of Cuneiform Studies. The American Schools of Oriental Research. 1947, 1 (3): 219–240, doi:10.2307/1359434 .
• Silver, A. L. Leigh, Musimatics or the nun's fiddle, American Mathematical Monthly. Mathematical Association of America. 1971, 78 (4): 351–357, doi:10.2307/2316896 .
• Størmer, Carl, Quelques théorèmes sur l'équation de Pell x2 - Dy2 = ±1 et leurs applications, Skrifter Videnskabs-selskabet (Christiania), Mat.-Naturv. Kl.. 1897, I (2) .
• Temperton, Clive, A generalized prime factor FFT algorithm for any N = 2p3q5r, SIAM Journal on Scientific and Statistical Computing. 1992, 13 (3): 676–686, doi:10.1137/0913039 .
• Yuen, C. K., Hamming numbers, lazy evaluation, and eager disposal, ACM SIGPLAN Notices. 1992, 27 (8): 71–75, doi:10.1145/142137.142151 .