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A number n is k-multiperfect (also called a k-multiply perfect number or k-pluperfect number) if sigma(n)=kn for some integer k>2, where sigma(n) is the divisor function. The ...

A riffle shuffle, also called the Faro shuffle, is a shuffle in which a deck of 2n cards is divided into two halves. The top half of the deck is placed in the left hand, and ...

Let b(k) be the number of 1s in the binary expression of k, i.e., the binary digit count of 1, giving 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, ... (OEIS A000120) for k=1, 2, .... ...

A symmetric graph is a graph that is both edge- and vertex-transitive (Holton and Sheehan 1993, p. 209). However, care must be taken with this definition since arc-transitive ...

A real number that is b-normal for every base 2, 3, 4, ... is said to be absolutely normal. As proved by Borel (1922, p. 198), almost all real numbers in [0,1) are absolutely ...

The lines connecting the vertices and corresponding circle-circle intersections in Malfatti's problem coincide in a point X_(179) called the first Ajima-Malfatti point ...

The above topological structure, composed of a countable union of compact sets, is called Alexander's horned sphere. It is homeomorphic with the ball B^3, and its boundary is ...

In most computer programs and computing environments, the precision of any calculation (even including addition) is limited by the word size of the computer, that is, by ...

An arithmetic series is the sum of a sequence {a_k}, k=1, 2, ..., in which each term is computed from the previous one by adding (or subtracting) a constant d. Therefore, for ...

A Banach space is a complete vector space B with a norm ||·||. Two norms ||·||_((1)) and ||·||_((2)) are called equivalent if they give the same topology, which is equivalent ...