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A cluster prime is a prime p such that every even natural number k ≤ p − 3 is the ... 10 p − 1 ≡ 1 ... All prime numbers from 31 to 6,469,693,189 for free ...
A number where some but not all prime factors have multiplicity above 1 is neither square-free nor squareful. 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 list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
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In mathematics an even integer, that is, a number that is divisible by 2, is called evenly even or doubly even if it is a multiple of 4, and oddly even or singly even if it is not. The former names are traditional ones, derived from ancient Greek mathematics ; the latter have become common in recent decades.
A number that has the same number of digits as the number of digits in its prime factorization, including exponents but excluding exponents equal to 1. A046758 Extravagant numbers
The parity function maps a number to the number of 1's in its binary representation, modulo 2, so its value is zero for evil numbers and one for odious numbers. The Thue–Morse sequence , an infinite sequence of 0's and 1's, has a 0 in position i when i is evil, and a 1 in that position when i is odious.
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