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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.
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Conversions between units in the metric system are defined by their prefixes (for example, 1 kilogram = 1000 grams, 1 milligram = 0.001 grams) and are thus not listed in this article. Exceptions are made if the unit is commonly known by another name (for example, 1 micron = 10 −6 metre).
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This template produces one row in a "family tree"-like chart consisting of boxes and connecting lines based loosely on an ASCII art-like syntax. It is meant to be used in conjunction with {{Tree chart/start}} and {{Tree chart/end}}. The chart is displayed as HTML tables using CSS attributes, and may contain arbitrary wiki markup within
Before performing a Yates analysis, the data should be arranged in "Yates' order". That is, given k factors, the k th column consists of 2 (k - 1) minus signs (i.e., the low level of the factor) followed by 2 (k - 1) plus signs (i.e., the high level of the factor). For example, for a full factorial design with three factors, the design matrix is
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
If each book had a mass of 100 grams, all of them would have a total mass of 10 93 kilograms. In comparison, Earth's mass is 5.97 × 10 24 kilograms [5], the mass of the Milky Way galaxy is estimated at 1.8 × 10 42 kilograms [6], and the total mass of all the stars in the observable universe is estimated at 2 × 10 52 kg. [7]