Pronic number
Number, product of consecutive integers / From Wikipedia, the free encyclopedia
A pronic number is a number that is the product of two consecutive integers, that is, a number of the form .[1] The study of these numbers dates back to Aristotle. They are also called oblong numbers, heteromecic numbers,[2] or rectangular numbers;[3] however, the term "rectangular number" has also been applied to the composite numbers.[4][5]
The first few pronic numbers are:
- 0, 2, 6, 12, 20, 30, 42, 56, 72, 90, 110, 132, 156, 182, 210, 240, 272, 306, 342, 380, 420, 462 … (sequence A002378 in the OEIS).
Letting denote the pronic number
, we have
. Therefore, in discussing pronic numbers, we may assume that
without loss of generality, a convention that is adopted in the following sections.