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A polygonal number of the form n(3n-1)/2. The first few are 1, 5, 12, 22, 35, 51, 70, ... (OEIS A000326). The generating function for the pentagonal numbers is ...

A sum-product number is a number n such that the sum of n's digits times the product of n's digit is n itself, for example 135=(1+3+5)(1·3·5). (1) Obviously, such a number ...

A number t_x=tan^(-1)(1/x)=cot^(-1)x, where x is an integer or rational number, tan^(-1)x is the inverse tangent, and cot^(-1)x is the inverse cotangent. Gregory numbers ...

A graph is said to be regular of degree r if all local degrees are the same number r. A 0-regular graph is an empty graph, a 1-regular graph consists of disconnected edges, ...

In the archaic terminology of Whittaker and Watson (1990), the complex number z representing x+iy.

The set theory symbol (aleph) for the cardinal number of a well-orderable infinite set.

A test which always identifies prime numbers correctly, but may incorrectly identify a composite number as a prime.

A cubic triangular number is a positive integer that is simultaneously cubic and triangular. Such a number must therefore satisfy T_n=m^3 for some positive integers n and m, ...

A number n is called an economical number if the number of digits in the prime factorization of n (including powers) uses fewer digits than the number of digits in n. The ...

A number which is simultaneously pentagonal and hexagonal. Let P_n denote the nth pentagonal number and H_m the mth hexagonal number, then a number which is both pentagonal ...