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The exponential factorial is defined by the recurrence relation a_n=n^(a_(n-1)), (1) where a_0=1. The first few terms are therefore a_1 = 1 (2) a_2 = 2^1=2 (3) a_3 = ...

A composite number defined analogously to a Smith number except that the sum of the number's digits equals the sum of the digits of its distinct prime factors (excluding 1). ...

Apply the 196-algorithm, which consists of taking any positive integer of two digits or more, reversing the digits, and adding to the original number. Now sum the two and ...

A series expansion is a representation of a particular function as a sum of powers in one of its variables, or by a sum of powers of another (usually elementary) function ...

Let the sum of squares function r_k(n) denote the number of representations of n by k squares, then the summatory function of r_2(k)/k has the asymptotic expansion ...

The Sombor matrix A_(Sombor) of a simple graph is a weighted adjacency matrix with weight f(d_i,d_j)=sqrt(d_i^2+d_j^2), (1) where d_i are the vertex degrees of the graph. In ...

Discrete Mathematics

Specifying three angles A, B, and C does not uniquely define a triangle, but any two triangles with the same angles are similar. Specifying two angles of a triangle ...

The ABC (atom-bond connectivity) index of a graph is defined as half the sum of the matrix elements of its ABC matrix. It was introduced by Estrada et al. (2017) to model the ...

There are two identities known as Catalan's identity. The first is F_n^2-F_(n+r)F_(n-r)=(-1)^(n-r)F_r^2, where F_n is a Fibonacci number. Letting r=1 gives Cassini's ...