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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 .
Multiplication table from 1 to 10 drawn to scale with the upper-right half labeled with prime factorisations. In mathematics, a multiplication table (sometimes, less formally, a times table) is a mathematical table used to define a multiplication operation for an algebraic system.
1: Picture a dog jumping over a shoe. 4: Picture a bottle of rum hanging from a tree. 1: Picture a tube connecting to a door. 5: Picture bees flying from a cup of lemonade as if it is a hive. 9: Picture a beetle climbing onto a chick nest. 2: Picture a newt with angel wings and a halo. 6: Picture a jaguar lifting weights.
Tally marks used in France, Portugal, Spain, and their former colonies, including Latin America. 1 to 5 and so on. These are most commonly used for registering scores in card games , like Truco . In the dot and line (or dot-dash) tally, dots represent counts from 1 to 4, lines 5 to 8, and diagonal lines 9 and 10.
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
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.