multiply perfect number | pluperfect number

A number n is k-multiperfect (also called a k-multiply perfect number or k-pluperfect number) if σ(n) = k n for some integer k>2, where σ(n) is the divisor function. The value of k is called the class. The special case k = 2 corresponds to perfect numbers P_2, which are intimately connected with Mersenne primes (OEIS A000396). The number 120 was long known to be 3-multiply perfect (P_3) since σ(120) = 3·120. The following table gives the first few P_n for n = 2, 3, ..., 6.

abundancy | e-multiperfect number | friendly pair | hyperperfect number | infinitary multiperfect number | Mersenne prime | perfect number | unitary multiperfect number