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Sociable numbers are numbers that result in a periodic aliquot sequence, where an aliquot sequence is the sequence of numbers obtained by repeatedly applying the restricted ...

A sultan has granted a commoner a chance to marry one of his n daughters. The commoner will be presented with the daughters one at a time and, when each daughter is ...

The toroidal crossing number cr_(1)(G) of a graph G is the minimum number of crossings with which G can be drawn on a torus. A planar graph has toroidal crossing number 0, ...

The Wigner 6j-symbols (Messiah 1962, p. 1062), commonly simply called the 6j-symbols, are a generalization of Clebsch-Gordan coefficients and Wigner 3j-symbol that arise in ...

Abstract Algebra

A perfect matching of a graph is a matching (i.e., an independent edge set) in which every vertex of the graph is incident to exactly one edge of the matching. A perfect ...

The smallest composite squarefree number (2·3), and the third triangular number (3(3+1)/2). It is the also smallest perfect number, since 6=1+2+3. The number 6 arises in ...

The area moment of inertia is a property of a two-dimensional plane shape which characterizes its deflection under loading. It is also known as the second moment of area or ...

A problem sometimes known as Moser's circle problem asks to determine the number of pieces into which a circle is divided if n points on its circumference are joined by ...

Contour integration is the process of calculating the values of a contour integral around a given contour in the complex plane. As a result of a truly amazing property of ...