正規數 (整數)

正規數（Regular numbers）是指可以整除60的乘冪的整數，也就是60乘冪的因數，例如60² = 3600 = 48 × 75，48和75都可以整除60的平方，也都是正規數。

一個400以內正規數其因數關係的哈斯圖，其縱向為對數尺度^[1]

在許多數學及應用的領域會用到60乘冪的因數，在不同的領域中其名稱也有所不同。

• 在數論中，60乘冪的因數也稱為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。
• 在巴比倫數學中，60乘冪的因數稱為正規數或是60正規數，因為巴比倫數學是使用六十進制，因此這類數字格外的重要。
• 在計算機科學，60乘冪的因數稱為漢明數（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乘冪的因數的演算法。

註釋

1. Inspired by similar diagrams by Erkki Kurenniemi in "Chords, scales, and divisor lattices" （頁面存檔備份，存於互聯網檔案館）.

參考資料

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