Perfect numbers

positive integer which equals the sum of all its divisors

prime number of the form 2ⁿ−1

positive integer that equals the sum of some of its proper divisors

number whose divisors add to a multiple of that number

theorem characterizing the even perfect numbers

sum of all proper divisors of a natural number

positive integer whose divisors have a harmonic mean that is an integer

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number with a half-integer abundancy index

natural number n for which the equality n=1+k(σ(n)−n−1) holds for some k

integer which is the sum of its positive proper unitary divisors, not including the number itself