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Two integers n and m<n are (alpha,beta)-multiamicable if sigma(m)-m=alphan and sigma(n)-n=betam, where sigma(n) is the divisor function and alpha,beta are positive integers. ...

A mapping of random number triples to points in spherical coordinates according to theta = 2piX_n (1) phi = piX_(n+1) (2) r = sqrt(X_(n+2)) (3) in order to detect unexpected ...

An extremely fast factorization method developed by Pollard which was used to factor the RSA-130 number. This method is the most powerful known for factoring general numbers, ...

Given a statistical distribution with measured mean, mode, and standard deviation sigma, the Pearson mode skewness is (mean-mode)/sigma. The function was incorrectly ...

Given a statistical distribution with measured mean, statistical median, mode, and standard deviation sigma, Pearson's first skewness coefficient, also known as the Pearson ...

Planck's's radiation function is the function f(x)=(15)/(pi^4)1/(x^5(e^(1/x)-1)), (1) which is normalized so that int_0^inftyf(x)dx=1. (2) However, the function is sometimes ...

A prime factorization algorithm which can be implemented in a single-step or double-step form. In the single-step version, a prime factor p of a number n can be found if p-1 ...

The factorization of a number into its constituent primes, also called prime decomposition. Given a positive integer n>=2, the prime factorization is written ...

Given an integer sequence {a_n}_(n=1)^infty, a prime number p is said to be a primitive prime factor of the term a_n if p divides a_n but does not divide any a_m for m<n. It ...

A Proth number that is prime, i.e., a number of the form N=k·2^n+1 for odd k, n a positive integer, and 2^n>k. Factors of Fermat numbers are of this form as long as they ...