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The conjecture proposed by Catalan in 1888 and extended by E. Dickson that each aliquot sequence ends in a prime, a perfect number, or a set of sociable numbers. The ...

The term perfect square is used to refer to a square number, a perfect square dissection, or a factorable quadratic polynomial of the form a^2+/-2ab+b^2=(a+/-b)^2.

A Poulet number whose divisors d all satisfy d|2^d-2. The first few are 341, 1387, 2047, 2701, 3277, 4033, 4369, 4681, 5461, 7957, 8321, ... (OEIS A050217).

A nonregular number, also called an infinite decimal (Havil 2003, p. 25), is a positive number that has an infinite decimal expansion. In contrast, a number that has a finite ...

A prime number (or prime integer, often simply called a "prime" for short) is a positive integer p>1 that has no positive integer divisors other than 1 and p itself. More ...

Algebraic number theory is the branch of number theory that deals with algebraic numbers. Historically, algebraic number theory developed as a set of tools for solving ...

A number n for which the product of divisors is equal to n^2. The first few are 1, 6, 8, 10, 14, 15, 21, 22, ... (OEIS A007422).

One of Cantor's ordinal numbers omega, omega+1, omega+2, ..., omega+omega, omega+omega+1, ... which is "larger" than any whole number.

A number n is called an e-perfect number if sigma_e(n)=2n, where sigma_e(n) is the sum of the e-Divisors of n. If m is squarefree, then sigma_e(m)=m. As a result, if n is ...

Lehmer's totient problem asks if there exist any composite numbers n such that phi(n)|(n-1), where phi(n) is the totient function? No such numbers are known. However, any ...