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A Liouville number is a transcendental number which has very close rational number approximations. An irrational number beta is called a Liouville number if, for each n, ...

An abundant number, sometimes also called an excessive number, is a positive integer n for which s(n)=sigma(n)-n>n, (1) where sigma(n) is the divisor function and s(n) is the ...

The Pell-Lucas numbers are the V_ns in the Lucas sequence with P=2 and Q=-1, and correspond to the Pell-Lucas polynomial Q_n(1). The Pell-Lucas number Q_n is equal to ...

A Münchhausen number (sometimes spelled Münchausen number, with a single 'h') is a number equal to the sum of its digits raised to each digit's power. Münchhausen numbers ...

An even perfect number is perfect number that is even, i.e., an even number n whose sum of divisors (including n itself) equals n. All known perfect numbers are even, and ...

Elementary number theory is the branch of number theory in which elementary methods (i.e., arithmetic, geometry, and high school algebra) are used to solve equations with ...

Consider the consecutive number sequences formed by the concatenation of the first n positive integers: 1, 12, 123, 1234, ... (OEIS A007908; Smarandache 1993, Dumitrescu and ...

A number of the form 2^n that contains the digits 666 (i.e., the beast number) is called an apocalyptic number. 2^(157) is an apocalyptic number. The first few such powers ...

An irrational number is a number that cannot be expressed as a fraction p/q for any integers p and q. Irrational numbers have decimal expansions that neither terminate nor ...

The number k in the expression s(n)=kn for a multiperfect number is called its class.