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In Book IX of The Elements, Euclid gave a method for constructing perfect numbers (Dickson 2005, p. 3), although this method applies only to even perfect numbers. In a 1638 ...

The prime number theorem gives an asymptotic form for the prime counting function pi(n), which counts the number of primes less than some integer n. Legendre (1808) suggested ...

Highly composite numbers are numbers such that divisor function d(n)=sigma_0(n) (i.e., the number of divisors of n) is greater than for any smaller n. Superabundant numbers ...

A floating-point number is a finite or infinite number that is representable in a floating-point format, i.e., a floating-point representation that is not a NaN. In the IEEE ...

A Pascal's triangle written in a square grid and padded with zeros, as written by Jakob Bernoulli (Smith 1984). The figurate number triangle therefore has entries a_(ij)=(i; ...

A polyhedron with extra triangular faces, given by the Schläfli symbol s{p; q}.

A figurate number of the form, CCub_n=n^3+(n-1)^3=(2n-1)(n^2-n+1). The first few are 1, 9, 35, 91, 189, 341, ... (OEIS A005898). The generating function for the centered cube ...

A multiplicative number theoretic function is a number theoretic function f that has the property f(mn)=f(m)f(n) (1) for all pairs of relatively prime positive integers m and ...

Given a Lyapunov characteristic exponent sigma_i, the corresponding Lyapunov characteristic number lambda_i is defined as lambda_i=e^(sigma_i). (1) For an n-dimensional ...

The numerators and denominators obtained by taking the ratios of adjacent terms in the triangular array of the number of +1 "bordered" alternating sign matrices A_n with a 1 ...