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The Wolstenholme numbers are defined as the numerators of the generalized harmonic number H_(n,2) appearing in Wolstenholme's theorem. The first few are 1, 5, 49, 205, 5269, ...

A prime p is called a Wolstenholme prime if the central binomial coefficient (2p; p)=2 (mod p^4), (1) or equivalently if B_(p-3)=0 (mod p), (2) where B_n is the nth Bernoulli ...

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 ...

The word "number" is a general term which refers to a member of a given (possibly ordered) set. The meaning of "number" is often clear from context (i.e., does it refer to a ...

A harmonic number is a number of the form H_n=sum_(k=1)^n1/k (1) arising from truncation of the harmonic series. A harmonic number can be expressed analytically as ...

Number Theory

An odd alternating permutation number, more commonly called an Euler number or secant number.

An even alternating permutation number, more commonly called a tangent number.

The algebraic integers in a number field.

A number n is called a k e-perfect number if sigma_e(n)=kn, where sigma_e(n) is the sum of the e-divisors of n.