abundant number

plural abundant numbers

1. mathematicsA number that is less than the sum of its proper divisors (all divisors except the number itself).

   The factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30, and 1 + 2 + 3 + 5 + 6 + 10 + 15 = 42, which is greater than 30, so 30 is an abundant number.

   3 more examples

   It has been shown that the largest odd number which cannot be written as the sum of two abundant numbers is 20161.

   1970, Geometric Transformations III, Random House, page 128

   1992, Stanley Rabinowitz (editor), Index to Mathematical Problems, 1980-1984, MathPro Press, page 185, (a) Let k be fixed. Do there exist sequences of k consecutive abundant numbers?

   We shall not be concerned with abundant numbers in this book, nevertheless it may be helpful to use this historical example as an illustration. We note the property that any multiple of an abundant number is abundant.

   1996, Richard R. Hall, Sets of Multiples, Cambridge University Press, page xi

   Synonyms: excessive number