User blog:DrCocktor/Angry number

The definition of an angry number has changed many times in the past. Currently, an angry number is any number n that follows the formula below.

Sigma(sigma(n)) = kn - 1

where sigma is the sum of the divisors of n, and k is a positive integer greater than 1.

Example: 75 is an angry number because the sum of the divisors of 75 is 1 + 3 + 5 + 15 + 25 + 75 = 124. The sum of the divisors of 124 is 1 + 2 + 4 31 + 62 + 124 = 224. 3 * 75 - 1 = 224, so in this case, k = 3, and therefore, 75 is an angry number.

Angry numbers are a generalization of almost perfect numbers. Just like the concept of m,k-perfect numbers, there is also the concept of m,k-almost perfect numbers. Almost perfect numbers are 1,2-almost perfect. Almost superperfect numbers are 2,2-almost perfect. (The only known almost superperfect number is 1). Angry numbers are 2,k-almost perfect for all k>1.