正规数(整数)

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求闻百科,共笔求闻
一个400以内正规数其因数关系的哈斯图,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乘幂的的因数,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乘幂的因数,在不同的领域中其名称也有所不同。

  • 数论中,60乘幂的因数也称为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乘幂的因数称为正规数或是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乘幂的因数称为汉明数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乘幂的因数的算法

注释

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

参考资料

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