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  2. Table of prime factors - Wikipedia

    en.wikipedia.org/wiki/Table_of_prime_factors

    The Liouville function λ(n) is 1 if Ω(n) is even, and is -1 if Ω(n) is odd. The Möbius function μ(n) is 0 if n is not square-free. Otherwise μ(n) is 1 if Ω(n) is even, and is −1 if Ω(n) is odd. A sphenic number has Ω(n) = 3 and is square-free (so it is the product of 3 distinct

  3. List of prime numbers - Wikipedia

    en.wikipedia.org/wiki/List_of_prime_numbers

    1 The first 1000 prime numbers. 2 Lists of primes by type. Toggle Lists of primes by type subsection. ... Of the form k×2 n + 1, with odd k and k < 2 n. 3, 5, ...

  4. Table of divisors - Wikipedia

    en.wikipedia.org/wiki/Table_of_divisors

    The tables below list all of the divisors of the numbers 1 to 1000. A divisor of an integer n is an integer m , for which n / m is again an integer (which is necessarily also a divisor of n ). For example, 3 is a divisor of 21, since 21/7 = 3 (and therefore 7 is also a divisor of 21).

  5. List of Mersenne primes and perfect numbers - Wikipedia

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

    So, 6 is a perfect number because the proper divisors of 6 are 1, 2, and 3, and 1 + 2 + 3 = 6. [2] [4] There is a one-to-one correspondence between the Mersenne primes and the even perfect numbers, but it is unknown whether there exist odd

  6. List of numbers - Wikipedia, the free encyclopedia

    en.wikipedia.org/wiki/List_of_numbers

    A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.

  7. Powerful number - Wikipedia

    en.wikipedia.org/wiki/Powerful_number

    Powerful numbers are also known as squareful, square-full, or 2-full. Paul Erdős and George Szekeres studied such numbers and Solomon W. Golomb named such numbers powerful. The following is a list of all powerful numbers between 1 and 1000:

  8. Odious number - Wikipedia

    en.wikipedia.org/wiki/Odious_number

    The odious numbers give the positions of the nonzero values in the Thue–Morse sequence. Every power of two is odious, because its binary expansion has only one nonzero bit. Except for 3, every Mersenne prime is odious, because its binary expansion consists of an odd prime number of consecutive nonzero bits.

  9. Highly abundant number - Wikipedia

    en.wikipedia.org/wiki/Highly_abundant_number

    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 of the divisors of any smaller natural number. Highly abundant numbers and several similar classes of numbers were first introduced by Pillai ( 1943 ), and early work on the subject was done by ...