根基

数论中,将正整数 n 的根基(英文:)定义为 n 的所有素因数(质因数)的积:

在不与开方运算里的“(root)”的概念混淆的情况下,也常简称“根”。例如我们有

所以506的根计算如下

整数的根运算对简化abc猜想的表述起到重要作用。[1]

根数列

所有正整数的根组成如下数列:

1, 2, 3, 2, 5, 6, 7, 2, 3, 10, 11, 6, 13, 14, 15, 2, 17, 6, 19, 10, 21, 22, 23, 6, 5, 26, 3, 14, 29, 30, 31, 2, 33, 34, 35, 6, 37, 38, 39, 10, 41, 42, 43, 22, 15, 46, 47, 6, 7, 10, ... OEIS中的数列A007947.

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参考资料

  1. Gowers, Timothy. . . Princeton University Press. 2008: 681.
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