abundant number

Definitions

1. 1

   A number that is less than the sum of its proper divisors (all divisors except the number…

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

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