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For example, 20 is a primitive abundant number because: The sum of its proper divisors is 1 + 2 + 4 + 5 + 10 = 22, so 20 is an abundant number. The sums of the proper divisors of 1, 2, 4, 5 and 10 are 0, 1, 3, 1 and 8 respectively, so each of these numbers is a deficient number. The first few primitive abundant numbers are:
The JScience library has a Complex number class. The JAS library allows the use of complex numbers. Netlib has a complex number class for Java. javafastcomplex also adds complex number support for Java; jcomplexnumber is a project on implementation of complex number in Java. JLinAlg includes complex numbers with arbitrary precision.
In computer science, primitive data types are a set of basic data types from which all other data types are constructed. [1] Specifically it often refers to the limited set of data representations in use by a particular processor , which all compiled programs must use.
There are infinitely many pseudoprimes to any given base a > 1. In 1904, Cipolla showed how to produce an infinite number of pseudoprimes to base a > 1: let A = (a p - 1)/(a - 1) and let B = (a p + 1)/(a + 1), where p is a prime number that does not divide a(a 2 - 1).
The aliquot sequence starting with a positive integer k can be defined formally in terms of the sum-of-divisors function σ 1 or the aliquot sum function s in the following way: [1] = = = > = = = If the s n-1 = 0 condition is added, then the terms after 0 are all 0, and all aliquot sequences would be infinite, and we can conjecture that all aliquot sequences are convergent, the limit of these ...
Primitive element (finite field), an element that generates the multiplicative group of a finite field; Primitive element (lattice), an element in a lattice that is not a positive integer multiple of another element in the lattice; Primitive element (coalgebra), an element X on which the comultiplication Δ has the value Δ(X) = X⊗1 + 1⊗X
Computing the Ackermann function can be restated in terms of an infinite table. First, place the natural numbers along the top row. To determine a number in the table, take the number immediately to the left. Then use that number to look up the required number in the column given by that number and one row up.
In statistics, a pivotal quantity or pivot is a function of observations and unobservable parameters such that the function's probability distribution does not depend on the unknown parameters (including nuisance parameters). [1]