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  2. Highly composite number - Wikipedia

    en.wikipedia.org/wiki/Highly_composite_number

    90 25 27720 3,2,1,1,1 8 ... Any factor of n must have the same or lesser multiplicity in each prime: ...

  3. Table of prime factors - Wikipedia

    en.wikipedia.org/wiki/Table_of_prime_factors

    m is a divisor of n (also called m divides n, or n is divisible by m) if all prime factors of m have at least the same multiplicity in n. 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 ...

  4. Composite number - Wikipedia

    en.wikipedia.org/wiki/Composite_number

    If none of its prime factors are repeated, it is called squarefree. (All prime numbers and 1 are squarefree.) For example, 72 = 2 3 × 3 2, all the prime factors are repeated, so 72 is a powerful number. 42 = 2 × 3 × 7, none of the prime factors are repeated, so 42 is squarefree. Euler diagram of numbers under 100:

  5. List of prime numbers - Wikipedia

    en.wikipedia.org/wiki/List_of_prime_numbers

    This is a list of articles about 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.

  6. Table of divisors - Wikipedia

    en.wikipedia.org/wiki/Table_of_divisors

    d() is the number of positive divisors of n, including 1 and n itself; σ() is the sum of the positive divisors of n, including 1 and n itselfs() is the sum of the proper divisors of n, including 1 but not n itself; that is, s(n) = σ(n) − n

  7. Smooth number - Wikipedia

    en.wikipedia.org/wiki/Smooth_number

    This definition includes numbers that lack some of the smaller prime factors; for example, both 10 and 12 are 5-smooth, even though they miss out the prime factors 3 and 5, respectively. All 5-smooth numbers are of the form 2 a × 3 b × 5 c , where a , b and c are non-negative integers.

  8. Integer factorization - Wikipedia

    en.wikipedia.org/wiki/Integer_factorization

    If one of the factors is composite, it can in turn be written as a product of smaller factors, for example 60 = 3 · 20 = 3 · (5 · 4). Continuing this process until every factor is prime is called prime factorization; the result is always unique up to the order of the factors by the prime factorization theorem.

  9. Fermat number - Wikipedia

    en.wikipedia.org/wiki/Fermat_number

    Yves Gallot's proth.exe has been used to find factors of large Fermat numbers. Édouard Lucas, improving Euler's above-mentioned result, proved in 1878 that every factor of the Fermat number , with n at least 2, is of the form + + (see Proth number), where k is a positive integer. By itself, this makes it easy to prove the primality of the ...