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The coefficients () ()! are called connection coefficients, and have a combinatorial interpretation as the number of ways to identify (or "glue together") k elements each from a set of size m and a set of size n.
Name First elements Short description OEIS Mersenne prime exponents : 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, ... Primes p such that 2 p − 1 is prime.: A000043 ...
42 is a pronic number, [1] an abundant number [2] as well as a highly abundant number, [3] a practical number, [4] an admirable number, [5] and a Catalan number. [6]The 42-sided tetracontadigon is the largest such regular polygon that can only tile a vertex alongside other regular polygons, without tiling the plane.
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 ...
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 ).
The third try produces the perfect square of 441. Thus, =, =, and the factors of 5959 are = and + =. Suppose N has more than two prime factors. That procedure first finds the factorization with the least values of a and b.
In combinatorics, a finite set with elements is sometimes called an -set and a subset with elements is called a -subset. For example, the set { 5 , 6 , 7 } {\displaystyle \{5,6,7\}} is a 3-set – a finite set with three elements – and { 6 , 7 } {\displaystyle \{6,7\}} is a 2-subset of it.
In number theory, the prime omega functions and () count the number of prime factors of a natural number . Thereby (little omega) counts each distinct prime factor, whereas the related function () (big omega) counts the total number of prime factors of , honoring their multiplicity (see arithmetic function).