在数论中，若一个正整数除了本身外之所有正因数之和比此数自身大，则称此数为过剩数。（又称作丰数或盈数）。

更为严格地说，过剩数是指使得函数 σ(n) > 2n的正整数，其中指的是因数和函数，即n的所有正因数（包括n）之和。σ(n) − 2n称作n的盈度。

例如12的正因数有 1,2,3,4,6,12，而1+2+3+4+6+12=28，28>122，所以12可称为过剩数。

最小的一些过剩数是： 12, 18, 20, 24, 30, 36, 40, 42, 48, 54, 56, 60, 66, 70, 72, 78, 80, 84, 88, 90, 96, 100, 102, …A005101

In number theory, an abundant number or excessive number is a number for which the sum of its proper divisors is greater than the number itself. The integer 12 is the first abundant number. Its proper divisors are 1, 2, 3, 4 and 6 for a total of 16. The amount by which the sum exceeds the number is the abundance. The number 12 has an abundance of 4, for example.