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A unitary perfect number is an integer which is the sum of its positive proper unitary divisors, not including the number itself. (A divisor d of a number n is a unitary divisor if d and n/d share no common factors). The number 6 is the only number that is both a perfect number and a unitary perfect number.
A hexagon also has 6 edges as well as 6 internal and external angles. 6 is the second smallest composite number. [1] It is also the first number that is the sum of its proper divisors, making it the smallest perfect number. [2] 6 is the first unitary perfect number, since it is the sum of its positive proper unitary divisors, without including ...
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]
The number of bi-unitary divisors of n is a multiplicative function of n with average order where [3] = ((+)) . A bi-unitary perfect number is one equal to the sum of its bi-unitary aliquot divisors. The only such numbers are 6, 60 and 90.
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A unitary multi 2-perfect number is naturally called a unitary perfect number. In the case k > 2, no example of a unitary multi k -perfect number is yet known. It is known that if such a number exists, it must be even and greater than 10 102 and must have more than forty four odd prime factors.
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