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Let sigma(m) be the divisor function of m. Then two numbers m and n are a quasiamicable pair if sigma(m)=sigma(n)=m+n+1. The first few are (48, 75), (140, 195), (1050, 1925), ...

A Gaussian quadrature-like formula for numerical estimation of integrals. It requires m+1 points and fits all polynomials to degree 2m, so it effectively fits exactly all ...

The vector space generated by the rows of a matrix viewed as vectors. The row space of a n×m matrix A with real entries is a subspace generated by n elements of R^m, hence ...

The concurrence S of the Euler lines E_n of the triangles DeltaXBC, DeltaXCA, DeltaXAB, and DeltaABC where X is the incenter. It has equivalent triangle center functions ...

tau(n) is prime for n=63001, 458329, 942841, 966289, 1510441, ... (OEIS A135430). These values are also known as Lehmer-Ramanujan numbers or LR numbers since the first of ...

A lattice polygon formed by a three-choice walk. The anisotropic perimeter and area generating function G(x,y,q)=sum_(m>=1)sum_(n>=1)sum_(a>=a)C(m,n,a)x^my^nq^a, where ...

A square matrix is said to be totally positive if the determinant of any square submatrix, including the minors, is positive. For instance, any 2×2 matrix whose determinant ...

The interior of the triangle is the set of all points inside a triangle, i.e., the set of all points in the convex hull of the triangle's vertices. The simplest way to ...

The union of two sets A and B is the set obtained by combining the members of each. This is written A union B, and is pronounced "A union B" or "A cup B." The union of sets ...

If p is a prime >3, then the numerator of the harmonic number H_(p-1)=1+1/2+1/3+...+1/(p-1) (1) is divisible by p^2 and the numerator of the generalized harmonic number ...