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[3] Perfect numbers are natural numbers that equal the sum of their positive proper divisors, which are divisors excluding the number itself. So, 6 is a perfect number because the proper divisors of 6 are 1, 2, and 3, and 1 + 2 + 3 = 6. [2] [4]
In number theory, a perfect number is a positive integer that is equal to the sum of its positive proper divisors, that is, divisors excluding the number itself. For instance, 6 has proper divisors 1, 2 and 3, and 1 + 2 + 3 = 6, so 6 is a perfect number. The next perfect number is 28, since 1 + 2 + 4 + 7 + 14 = 28.
It can be proven that: . For a given prime number p, if n is p-perfect and p does not divide n, then pn is (p + 1)-perfect.This implies that an integer n is a 3-perfect number divisible by 2 but not by 4, if and only if n/2 is an odd perfect number, of which none are known.
A perfect number is a natural number that equals the sum of its proper divisors, the numbers that are less than it and divide it evenly (with remainder zero). For instance, the proper divisors of 6 are 1, 2, and 3, which sum to 6, so 6 is perfect. A Mersenne prime is a prime number of the form M p = 2 p − 1, one less than a power of two.
The aliquot sum function can be used to characterize several notable classes of numbers: 1 is the only number whose aliquot sum is 0. A number is prime if and only if its aliquot sum is 1. [1] The aliquot sums of perfect, deficient, and abundant numbers are equal to, less than, and greater than the number itself respectively. [1]
The sum of positive divisors ... p 2 is 3); noting that 24 is the product of 2 3 ×3 1, a 1 is 3 and a 2 ... This function is used to recognize perfect numbers, ...
A unitary perfect number is an integer which is the sum of its positive proper ... perfect number because 1, 3, 4, 5, 12, 15, and 20 are its proper unitary divisors ...
The sum of the reciprocals of all perfect powers including duplicates (but not including 1) equals 1. The Erdős–Moser equation, + + + = (+) where m and k are positive integers, is conjectured to have no solutions other than 1 1 + 2 1 = 3 1.