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An abundant number, sometimes also called an excessive number, is a positive integer n for which s(n)=sigma(n)-n>n, (1) where sigma(n) is the divisor function and s(n) is the ...

Let n be a positive nonsquare integer. Then Artin conjectured that the set S(n) of all primes for which n is a primitive root is infinite. Under the assumption of the ...

A modified set of Chebyshev polynomials defined by a slightly different generating function. They arise in the development of four-dimensional spherical harmonics in angular ...

Checkers is a two-player game with the most common variant played on an 8×8 checkerboard with each player starts with twelve pieces of a fixed color on opposite sites of the ...

A commutative diagram is a collection of maps A_i-->^(phi_i)B_i in which all map compositions starting from the same set A and ending with the same set B give the same ...

The cosine function cosx is one of the basic functions encountered in trigonometry (the others being the cosecant, cotangent, secant, sine, and tangent). Let theta be an ...

Eigenvectors are a special set of vectors associated with a linear system of equations (i.e., a matrix equation) that are sometimes also known as characteristic vectors, ...

In response to a letter from Goldbach, Euler considered sums of the form s_h(m,n) = sum_(k=1)^(infty)(1+1/2+...+1/k)^m(k+1)^(-n) (1) = ...

An Eulerian graph is a graph containing an Eulerian cycle. The numbers of Eulerian graphs with n=1, 2, ... nodes are 1, 1, 2, 3, 7, 15, 52, 236, ... (OEIS A133736), the first ...

The sum-of-factorial powers function is defined by sf^p(n)=sum_(k=1)^nk!^p. (1) For p=1, sf^1(n) = sum_(k=1)^(n)k! (2) = (-e+Ei(1)+pii+E_(n+2)(-1)Gamma(n+2))/e (3) = ...