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The nth Ramanujan prime is the smallest number R_n such that pi(x)-pi(x/2)>=n for all x>=R_n, where pi(x) is the prime counting function. In other words, there are at least n ...

Following Ramanujan (1913-1914), write product_(k=1,3,5,...)^infty(1+e^(-kpisqrt(n)))=2^(1/4)e^(-pisqrt(n)/24)G_n (1) ...

In a plane, consider a sum of N two-dimensional vectors with random orientations. Use phasor notation, and let the phase of each vector be random. Assume N unit steps are ...

A number n is said to be refactorable, sometimes also called a tau number (Kennedy and Cooper 1990), if it is divisible by the number of its divisors sigma_0(n), where ...

A prime which does not divide the class number h(p) of the cyclotomic field obtained by adjoining a primitive pth root of unity to the field of rationals. A prime p is ...

According to most authors (e.g., Kelley 1955, p. 113; McCarty 1967, p. 144; Willard 1970, p. 92) a regular space is a topological space in which every neighborhood of a point ...

Robertson's apex graph is the 15-vertex graph illustrated above constructed by Neil Robertson as an example of an apex graph that is not YDeltaY-reducible. The graph may be ...

If n>19, there exists a Poulet number between n and n^2. The theorem was proved in 1965.

The S distribution is defined in terms of its distribution function F(x) as the solution to the initial value problem (dF)/(dx)=alpha(F^g-F^h), where F(x_0)=F_0 (Savageau ...

When computing the sample variance s numerically, the mean must be computed before s^2 can be determined. This requires storing the set of sample values. However, it is ...