colossally abundant number
An integer is a colossally abundant number if there is an exponent such that the sum of divisors of divided by raised to that exponent is greater than or equal to the sum of divisors of any other integer divided by raised to that same exponent. That is,
with being the sum of divisors function.
The first few colossally abundant numbers are 1, 2, 6, 12, 60, 120, 360, 2520, 5040, 55440, 720720, 1441440, 4324320. The index of a colossally abundant number is equal to the number of its nondistinct prime factors, that is to say that for the th colossally abundant number the equality is true.
|Title||colossally abundant number|
|Date of creation||2013-03-22 17:37:52|
|Last modified on||2013-03-22 17:37:52|
|Last modified by||CompositeFan (12809)|