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  2. Table of divisors - Wikipedia

    en.wikipedia.org/wiki/Table_of_divisors

    a highly abundant number has a sum of positive divisors that is greater than any lesser number; that is, σ(n) > σ(m) for every positive integer m < n. Counterintuitively, the first seven highly abundant numbers are not abundant numbers. a prime number has only 1 and itself as divisors; that is, d(n) = 2

  3. List of Mersenne primes and perfect numbers - Wikipedia

    en.wikipedia.org/wiki/List_of_Mersenne_primes...

    Perfect numbers are natural numbers that equal the sum of their positive proper divisors, which are divisors excluding the number itself. So, 6 is a perfect number because the proper divisors of 6 are 1, 2, and 3, and 1 + 2 + 3 = 6. [2] [4]

  4. Divisor - Wikipedia

    en.wikipedia.org/wiki/Divisor

    Divisors can be negative as well as positive, although often the term is restricted to positive divisors. For example, there are six divisors of 4; they are 1, 2, 4, −1, −2, and −4, but only the positive ones (1, 2, and 4) would usually be mentioned. 1 and −1 divide (are divisors of) every integer.

  5. List of prime numbers - Wikipedia

    en.wikipedia.org/wiki/List_of_prime_numbers

    A prime number (or prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. By Euclid's theorem , there are an infinite number of prime numbers. Subsets of the prime numbers may be generated with various formulas for primes .

  6. List of integer sequences - Wikipedia

    en.wikipedia.org/wiki/List_of_integer_sequences

    A positive integer with more divisors than any smaller positive integer. A002182: Superior highly composite numbers: 2, 6, 12, 60, 120, 360, 2520, 5040, 55440, 720720, ... A positive integer n for which there is an e > 0 such that ⁠ d(n) / n e ⁠ ≥ ⁠ d(k) / k e ⁠ for all k > 1. A002201: Pronic numbers: 0, 2, 6, 12, 20, 30, 42, 56, 72 ...

  7. Table of prime factors - Wikipedia

    en.wikipedia.org/wiki/Table_of_prime_factors

    The divisors of n are all products of some or all prime factors of n (including the empty product 1 of no prime factors). The number of divisors can be computed by increasing all multiplicities by 1 and then multiplying them. Divisors and properties related to divisors are shown in table of divisors.

  8. Divisor function - Wikipedia

    en.wikipedia.org/wiki/Divisor_function

    Divisor function σ 0 (n) up to n = 250 Sigma function σ 1 (n) up to n = 250 Sum of the squares of divisors, σ 2 (n), up to n = 250 Sum of cubes of divisors, σ 3 (n) up to n = 250. In mathematics, and specifically in number theory, a divisor function is an arithmetic function related to the divisors of an integer.

  9. Arithmetic function - Wikipedia

    en.wikipedia.org/wiki/Arithmetic_function

    An example of an arithmetic function is the divisor function whose value at a positive integer n is equal to the number of divisors of n. Arithmetic functions are often extremely irregular (see table ), but some of them have series expansions in terms of Ramanujan's sum .