An abundant number, sometimes also called an excessive number, is a positive integer n for which s(n)=sigma(n)-n>n, (1) where sigma(n) is the divisor function and s(n) is the restricted divisor function. The quantity sigma(n)-2n is sometimes called the abundance. A number which is abundant but for which all its proper divisors are deficient is called a primitive abundant number (Guy 1994, p. 46). The first few abundant numbers are 12, 18, 20, 24, 30, 36, ... (OEIS A005101). Every positive integer n with (mod n)60 is abundant. Any multiple of a perfect number or an abundant number is also abundant. Prime numbers are not abundant. Every number greater than 20161 can be expressed as a sum of two abundant numbers. There are only 21 abundant numbers less than 100, and they are all even. The first odd abundant number is 945=3^3·7·5. (2) That 945 is abundant can be seen by computing s(945)=975>945. (3) AbundantNumberDensity Define the density function A(x)=lim_(n->infty)(|{k<=n:sigma(k)>=xk}|)/n (4) (correcting the expression in Finch 2003, p. 126) for a positive real number x where |B| gives the cardinal number of the set B, then Davenport (1933) proved that A(x) exists and is continuous for all x, and Erdős (1934) gave a simplified proof (Finch 2003). The special case A(2) then gives the asymptotic density of abundant numbers,
If the triangles are similar, then the sides are proportionate and the bases are as well. Set up the proportion like this, with side lengths on top and base lengths on bottom: . Cross multiply to get 4x = 60. That means that x = 20.