What is a near perfect number?
In mathematics, an almost perfect number (sometimes also called slightly defective or least deficient number) is a natural number n such that the sum of all divisors of n (the sum-of-divisors function σ(n)) is equal to 2n − 1, the sum of all proper divisors of n, s(n) = σ(n) − n, then being equal to n − 1.
List of perfect numbers
- The usual ordinal form is "twelfth" but "dozenth" or "duodecimal" (from the Latin word) is also used in some contexts, particularly base-12 numeration. Similarly, a group of twelve things is usually a "dozen" but may also be referred to as a "duodecad".
- Zero has one square root which is 0. Negative numbers don't have real square roots since a square is either positive or 0. The square roots of numbers that are not a perfect square are members of the irrational numbers. This means that they can't be written as the quotient of two integers.
- In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, √9 = 3, so 9 is a square number. A positive integer that has no perfect square divisors except 1 is called square-free.
A number is perfect if the sum of its proper factors is equal to the number. To find the proper factors of a number, write down all numbers that divide the number with the exception of the number itself. If the sum of the factors is equal to 18, then 18 is a perfect number. The first 10 perfect numbers are shown below.
- Amicable numbers are two different numbers so related that the sum of the proper divisors of each is equal to the other number. (A proper divisor of a number is a positive factor of that number other than the number itself. For example, the proper divisors of 6 are 1, 2, and 3.)
- List of perfect numbers
Rank p Perfect number 2 3 28 3 5 496 4 7 8128 5 13 33550336
- A perfect number is defined to be one which is equal to the sum of its aliquot parts. The four perfect numbers 6, 28, 496 and 8128 seem to have been known from ancient times and there is no record of these discoveries.
A perfect number is defined to be one which is equal to the sum of its aliquot parts. The four perfect numbers 6, 28, 496 and 8128 seem to have been known from ancient times and there is no record of these discoveries.
- Perfect numbers are positive integers that are the sum of their proper divisors. For instance, 6 is a perfect number, because the sum of its proper divisors, 1, 2, and 3 equals 6 (1 + 2 + 3 = 6). Furthermore, in the letter, Descartes was the first to reason that an odd perfect number may or may not exist.
- If is also a prime, then it is known as a Mersenne Prime. It is well known from Euclid's proof that there exist infinitely many regular primes. However, for some special sets of prime numbers (Mersenne Primes, Sophie-Germain Primes, Twin Primes, etc.) this question has never been answered.
- Strong number: Strong numbers are the numbers whose sum of factorial of digits is equal to the original number. Example: 145 is a strong number. Since 1!
Updated: 3rd September 2018