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The number d(n) of monotone Boolean functions of n variables (equivalent to one more than the number of antichains on the n-set {1,2,...,n}) is called the nth Dedkind number. ...

The Schur number S(k) is the largest integer n for which the interval [1,n] can be partitioned into k sum-free sets (Fredricksen and Sweet 2000). S(k) is guaranteed to exist ...

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 ...

In common usage, an ordinal number is an adjective which describes the numerical position of an object, e.g., first, second, third, etc. In formal set theory, an ordinal ...

For any ideal I in a Dedekind ring, there is an ideal I_i such that II_i=z, (1) where z is a principal ideal, (i.e., an ideal of rank 1). Moreover, for a Dedekind ring with a ...

A Keith number is an n-digit integer N>9 such that if a Fibonacci-like sequence (in which each term in the sequence is the sum of the n previous terms) is formed with the ...

A polygonal number of the form O_n=n(3n-2). The first few are 1, 8, 21, 40, 65, 96, 133, 176, ... (OEIS A000567). The generating function for the octagonal numbers is ...

A polygonal number of the form n(5n-3)/2. The first few are 1, 7, 18, 34, 55, 81, 112, ... (OEIS A000566). The generating function for the heptagonal numbers is ...

A number of the form 2^n-1 obtained by setting x=1 in a Fermat-Lucas polynomial, more commonly known as a Mersenne number.

A figurate number which is equal to the cubic number n^3. The first few are 1, 8, 27, 64, ... (OEIS A000578).