In number theory, a colossally abundant number (sometimes abbreviated as CA) is a natural number that, in a particular, rigorous sense, has many divisors...

In number theory, a highly abundant number is a natural number with the property that the sum of its divisors (including itself) is greater than the sum...

natural number following 5039 and preceding 5041. It is a factorial (7!), a superior highly composite number, abundant number, colossally abundant number and...

In number theory, an abundant number or excessive number is a positive integer for which the sum of its proper divisors is greater than the number. The...

280 = harmonic divisor number 1,441,440 = colossally abundant number, superior highly composite number 1,441,889 = Markov number 1,500,625 = 12252 = 354...

highly composite number. a colossally abundant number. the last highly composite number that is half of the next highly composite number. the last highly...

primitive abundant number is an abundant number whose proper divisors are all deficient numbers. For example, 20 is a primitive abundant number because:...

highly composite number; colossally abundant number; smallest number divisible by the numbers from 1 to 16 725,760 = highly totient number 726,180 = harmonic...

and colossally abundant. It is also a sparsely totient number. 120 is also the smallest highly composite number with no adjacent prime number, being...

chiliagonal number 55296 = 3-smooth number 55440 = superior highly composite number; colossally abundant number 55459 = one of five remaining Seventeen...

superior highly composite number, a colossally abundant number, a refactorable number, a 5-smooth number, and a Harshad number in decimal since the sum...

number 225,331,713 = self-descriptive number in base 9 229,345,007 = 475 232,792,560 = superior highly composite number; colossally abundant number;...

178 6,983,776,800 = 15th colossally abundant number, 15th superior highly composite number 7,007,009,909 = smallest number in base 10 to take 100 iterations...

10, and 12; colossally abundant number; Harshad number in several bases. It is also the highest number with more divisors than any number less than double...

684 21,531,778 = Markov number 21,621,600 = colossally abundant number, superior highly composite number 22,222,222 = repdigit 22,235,661 = 33×77 22,667...

Kevin A.; Zhou, Qizhi (2008). "Odd multiperfect numbers of abundancy 4" (PDF). Journal of Number Theory. 126 (6): 1566–1575. doi:10.1016/j.jnt.2007.02.001...

semiperfect number is 945 (see, e.g., Friedman 1993). A semiperfect number is necessarily either perfect or abundant. An abundant number that is not semiperfect...

A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has...

A cyclic number is an integer for which cyclic permutations of the digits are successive integer multiples of the number. The most widely known is the...

In number theory, a weird number is a natural number that is abundant but not semiperfect. In other words, the sum of the proper divisors (divisors including...

The first 15 superabundant numbers are the same as the first 15 colossally abundant numbers. In decimal, 15 contains the digits 1 and 5 and is the result...

perfect number. Most abundant numbers are also semiperfect; abundant numbers which are not semiperfect are called weird numbers. Hyperperfect number Leinster...

In number theory, a happy number is a number which eventually reaches 1 when replaced by the sum of the square of each digit. For instance, 13 is a happy...

A nonagonal number, or an enneagonal number, is a figurate number that extends the concept of triangular and square numbers to the nonagon (a nine-sided...

with σ(n) = 2n, and abundant numbers with σ(n) > 2n. Nicomachus was the first to subdivide numbers into deficient, perfect, or abundant, in his Introduction...

polygonal number a number represented as a discrete r-dimensional regular geometric pattern of r-dimensional balls such as a polygonal number (for r =...

A heptagonal number is a figurate number that is constructed by combining heptagons with ascending size. The n-th heptagonal number is given by the formula...

superabundant number (Akbary & Friggstad 2009). Not all superabundant numbers are colossally abundant. The generalized k {\displaystyle k} -super abundant numbers...

In mathematics, a harshad number (or Niven number) in a given number base is an integer that is divisible by the sum of its digits when written in that...

In mathematics, the Fibonacci sequence is a sequence in which each number is the sum of the two preceding ones. Numbers that are part of the Fibonacci...