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By way of analogy with the eban numbers, oban numbers are defined as numbers whose English names do not contain the letter "o" (i.e., "o" is banned). Note that this ...

A "visual representation" number which is a sum of some simple function of its digits. For example, 1233 = 12^2+33^2 (1) 2661653 = 1653^2-266^2 (2) 221859 = 22^3+18^3+59^3 ...

Numbers which are not perfect and for which s(N)=sigma(N)-N<N, or equivalently sigma(n)<2n, where sigma(N) is the divisor function. Deficient numbers are sometimes called ...

A figurate number of the form g_n=2n-1 giving the area of the square gnomon obtained by removing a square of side n-1 from a square of side n, g_n = n^2-(n-1)^2 (1) = 2n-1. ...

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 cyclic number is an (n-1)-digit integer that, when multiplied by 1, 2, 3, ..., n-1, produces the same digits in a different order. Cyclic numbers are generated by the full ...

A congruent number can be defined as an integer that is equal to the area of a rational right triangle (Koblitz 1993). Numbers (a,x,y,z,t) such that {x^2+ay^2=z^2; ...

The Pell numbers are the numbers obtained by the U_ns in the Lucas sequence with P=2 and Q=-1. They correspond to the Pell polynomial P_n(x) and Fibonacci polynomial F_n(x) ...

Sequences of integers generated in the Collatz problem. For example, for a starting number of 7, the sequence is 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, ...

A number k such that nk^2 has its last digit(s) equal to k is called n-automorphic. For example, 1·5__^2=25__ (Wells 1986, pp. 58-59) and 1·6__^2=36__ (Wells 1986, p. 68), so ...