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Define the abundancy Sigma(n) of a positive integer n as Sigma(n)=(sigma(n))/n, (1) where sigma(n) is the divisor function. Then a pair of distinct numbers (k,m) is a ...

A set of two numbers or objects linked in some way is said to be a pair. The pair a and b is usually denoted (a, b), and is generally considered to be ordered, making it a ...

A friendly number is a number that is a member of a friendly pair or a higher-order friendly n-tuple. Numbers that are not friendly are said to be solitary. There are some ...

An amicable pair (m,n) consists of two integers m,n for which the sum of proper divisors (the divisors excluding the number itself) of one number equals the other. Amicable ...

A pair of quantities (a, b) where ordering is significant, so (a, b) is considered distinct from (b, a) for a!=b.

Given an amicable pair (m,n), the quantity sigma(m) = sigma(n) (1) = =s(m)+s(n) (2) = m+n (3) is called the pair sum, where sigma(n) is the divisor function and s(n) is the ...

A pair of zips, each zip being half a zipper, which can be zippered up to close a surface along a curve. The concept of a zip-pair can be extremely useful in topological ...

Let x->y and u->v be two rules of a term rewriting system, and suppose these rules have no variables in common. If they do, rename the variables. If x_1 is a subterm of x (or ...

Two objects form a mirror pair if one can be translated and rotated in such a way that the two objects together possess mirror symmetry, i.e., one is the mirror image of the ...

An ordered pair (a,b) of nonnegative integers such that there is some set of a points and b edges whose removal disconnects the graph and there is no set of a-1 nodes and b ...