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The upper domination number Gamma(G) of a graph G is the maximum size of a minimal dominating set of vertices in G. The (lower) domination number may be similarly defined as ...

An (n,k)-talisman hexagon is an arrangement of nested hexagons containing the integers 1, 2, ..., H_n=3n(n-1)+1, where H_n is the nth hex number, such that the difference ...

An Achilles number is a positive integer that is powerful (in the sense that each prime factor occurs with exponent greater than one) but imperfect (in the sense that the ...

A positive integer which is divisible by the sum of its digits, also called a Niven number (Kennedy et al. 1980) or a multidigital number (Kaprekar 1955). The first few are ...

The field of all rational and irrational numbers is called the real numbers, or simply the "reals," and denoted R. The set of real numbers is also called the continuum, ...

The number one (1), also called "unity," is the first positive integer. It is an odd number. Although the number 1 used to be considered a prime number, it requires special ...

Let s(n)=sigma(n)-n, where sigma(n) is the divisor function and s(n) is the restricted divisor function, and define the aliquot sequence of n by ...

An n-persistent number is a positive integer k which contains the digits 0, 1, ..., 9 (i.e., is a pandigital number), and for which 2k, ..., nk also share this property. No ...

To define a recurring digital invariant of order k, compute the sum of the kth powers of the digits of a number n. If this number n^' is equal to the original number n, then ...

A double Mersenne number is a number of the form M_(M_n)=2^(2^n-1)-1, where M_n is a Mersenne number. The first few double Mersenne numbers are 1, 7, 127, 32767, 2147483647, ...