Abundant number

A natural number is called abundant (Latin Abundans " overloaded " ) if their sum of proper divisors is (the sum of all divisors excluding the number itself ) is greater than the number itself

The smallest abundant number is 12 (1 2 3 4 6 = 16> 12). Are the first straight abundant numbers

The smallest abundant number that is not divisible by 3 is 20 (1 2 4 5 10 = 22 > 20)

The smallest odd abundant number is 945 (1 3 5 7 9 15 21 27 35 45 63 105 135 189 315 = 975 > 945). The first odd abundant numbers are

The smallest odd abundant number that is not divisible by 3, is = 5391411025 ( 5.5.7.11.13.17.19.23.29 )

The lowest abundant number is divisible by n, is at the most 6n (1 2 3 6 n 2 n 3n = 6n 12 > 6n)

If the divisor sum, however, equal to the number, it is called a perfect number. 6 ( 1 2 3 = 6) and 28, the first of these figures, (1 2 4 7 14 = 28). If the divisor sum is less, then one speaks of a deficient number. (1 2 4 < 8); (1 2 5 < 10)

A number n is called simple abundant if the sum of its proper divisors yields equal to n 1. The question of whether there is a slightly abundant number is unknown as yet.