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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
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. Subsets of the prime numbers may be generated with various formulas for primes.
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).
This page was last edited on 28 September 2007, at 23:06 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may apply.
Klauber's 1932 paper describes a triangle in which row n contains the numbers (n − 1) 2 + 1 through n 2. As in the Ulam spiral, quadratic polynomials generate numbers that lie in straight lines. Vertical lines correspond to numbers of the form k 2 − k + M. Vertical and diagonal lines with a high density of prime numbers are evident in the ...
1566 = number k such that k 64 + 1 is prime; 1567 = number of partitions of 24 with at least one distinct part [200] 1568 = Achilles number [343] 1569 = 2 × 28 2 + 1 = number of different 2 × 2 determinants with integer entries from 0 to 28 [199] 1570 = 2 × 28 2 + 2 = number of points on surface of tetrahedron with edgelength 28 [141] 1571 ...
This is a list of all articles about natural numbers from 1 to 10,000. Red links are included to make it clearly visible which articles exist and which do not. Existing articles can either be articles with content, or redirects .
Even-Odd as an early form of roulette. This game was known by the Greeks (as artiazein) and Romans (as ludere par impar).In the 1858 Krünitzlexikon it says: [3] "The game Odds and Evens was very common amongst the Romans and was played either with tali, tesseris, or money and known as "Alea maior", or with nuts, beans and almonds and known as "Alea minor"."
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