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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.
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.
25.4 μm. A thousandth of an inch is a derived unit of length in a system of units using inches. Equal to 1000 of an inch, a thousandth is commonly called a thou / ˈθaʊ / (used for both singular and plural) or, particularly in North America, a mil (plural mils ). The words are shortened forms of the English and Latin words for "thousand ...
Table of divisors. Plot of the number of divisors of integers from 1 to 1000. Highly composite numbers are in bold and superior highly composite numbers are starred. In the SVG file, hover over a bar to see its statistics. 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 ...
This section illustrates several systems for naming large numbers, and shows how they can be extended past vigintillion . Traditional British usage assigned new names for each power of one million (the long scale ): 1,000,000 = 1 million; 1,000,0002 = 1 billion; 1,000,0003 = 1 trillion; and so on. It was adapted from French usage, and is ...
1000 is the element of multiplicity in a toroidal board in the n -Queens problem, [ 8] with respective indicator of 25 [ 9] and count of 51. [ 10][ 11] 1000 is the number of strict partitions of 50 containing the sum of no subset of the parts.
Number ones. The Bee Gees scored the most number-one hits (9 songs) and had the longest cumulative run atop the Billboard Hot 100 chart (27 weeks) during the 1970s. Rod Stewart remained at the top of the Billboard Hot 100 chart for 17 weeks during the 1970s. Elton John amassed the second-most number-one hits on the Hot 100 chart during the ...
This is a list of NGC objects 1–1000 from the New General Catalogue (NGC). The astronomical catalogue is composed mainly of star clusters, nebulae, and galaxies.