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The multiplicity of a prime which does not divide n may be called 0 or may be considered undefined. Ω(n), the prime omega function, is the number of prime factors of n counted with multiplicity (so it is the sum of all prime factor multiplicities). A prime number has Ω(n) = 1.
2.40 Pell primes. 2.41 Permutable ... write the prime factorization of n in base 10 and concatenate the factors; iterate until a prime is reached. 2, 3, 211, 5, 23, 7 ...
40 is an abundant number.. Swiss mathematician Leonhard Euler noted 40 prime numbers generated by the quadratic polynomial + +, with values =,,,...,.These forty prime numbers are the same prime numbers that are generated using the polynomial + with values of from 1 through 40, and are also known in this context as Euler's "lucky" numbers.
The same prime factor may occur more than once; this example has two copies of the prime factor When a prime occurs multiple times, exponentiation can be used to group together multiple copies of the same prime number: for example, in the second way of writing the product above, 5 2 {\displaystyle 5^{2}} denotes the square or second power of ...
40 18 2520* 3,2,1,1 7 ... Roughly speaking, for a number to be highly composite it has to have prime factors as small as possible, but not too many of the same.
In number theory, the prime omega functions and () count the number of prime factors of a natural number . The number of distinct prime factors is assigned to ω ( n ) {\displaystyle \omega (n)} (little omega), while Ω ( n ) {\displaystyle \Omega (n)} (big omega) counts the total number of prime factors with multiplicity (see arithmetic ...
Thus, when + is prime, the first factor in the product becomes one, and the formula ... For n = 40, it produces a square number, 1681, ...
If one of the factors is composite, it can in turn be written as a product of smaller factors, for example 60 = 3 · 20 = 3 · (5 · 4). Continuing this process until every factor is prime is called prime factorization; the result is always unique up to the order of the factors by the prime factorization theorem.