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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. The first: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37 (sequence A000040 in the OEIS ).
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.
In mathematics, factorization (or factorisation, see English spelling differences) or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind. For example, 3 × 5 is an integer factorization of 15, and (x – 2)(x + 2) is a polynomial ...
The numbers that end with other digits are all composite: decimal numbers that end in 0, 2, 4, 6, or 8 are even, and decimal numbers that end in 0 or 5 are divisible by 5. [ 11 ] The set of all primes is sometimes denoted by P {\displaystyle \mathbf {P} } (a boldface capital P) [ 12 ] or by P {\displaystyle \mathbb {P} } (a blackboard bold ...
Such a number is a divisor of (⌈ / ⌉,,). The regular numbers are also called 5-smooth, indicating that their greatest prime factor is at most 5. [2] More generally, a k-smooth number is a number whose greatest prime factor is at most k. [3] The first few regular numbers are [2]
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In mathematics, a Ruth–Aaron pair consists of two consecutive integers (e.g., 714 and 715) for which the sums of the prime factors of each integer are equal: 714 = 2 × 3 × 7 × 17, 715 = 5 × 11 × 13,
As 120 is a factorial and one less than a square (! =), it—with 11—is one of the few Brown number pairs. 120 appears in Pierre de Fermat's modified Diophantine problem as the largest known integer of the sequence 1, 3, 8, 120. Fermat wanted to find another positive integer that, when multiplied by any of the other numbers in the sequence ...
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