多重完全数（multiply perfect number）为一数学名词，是一种广义的完全数。

针对一自然数k，自然数n为k重完全数的充份必要条件是n所有正因数的和（即除数函数，σ(n)）等于n的k倍，此定义下，完全数的除数函数为本身的2倍，因此是2重完全数。不论k的数值为何，k重完全数都属于多重完全数。至2004年7月为止．已经找到k为11的多重完全数。

可以证明：

In mathematics, a multiply perfect number (also called multiperfect number or pluperfect number) is a generalization of a perfect number.

For a given natural number k, a number n is called k-perfect (or k-fold perfect) if and only if the sum of all positive divisors of n (the divisor function, σ(n)) is equal to kn; a number is thus perfect if and only if it is 2-perfect. A number that is k-perfect for a certain k is called a multiply perfect number. As of 2014, k-perfect numbers are known for each value of k up to 11.