A pronic number is a number that is the product of two consecutive integers, that is, a number of the form <math>n(n+1)</math>. The study of these numbers dates back to Aristotle. They are also called oblong numbers, heteromecic numbers, or rectangular numbers;
The first 60 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, 506, 552, 600, 650, 702, 756, 812, 870, 930, 992, 1056, 1122, 1190, 1260, 1332, 1406, 1482, 1560, 1640, 1722, 1806, 1892, 1980, 2070, 2162, 2256, 2352, 2450, 2550, 2652, 2756, 2862, 2970, 3080, 3192, 3306, 3422, 3540, 3660... .
Letting <math>P_n</math> denote the pronic number <math>n(n+1)</math>, we have <math>P_\rfloor \cdot \lceil{\sqrt{m\rceil = m.</math>
The fact that consecutive integers are coprime and that a pronic number is the product of two consecutive integers leads to a number of properties. Each distinct prime factor of a pronic number is present in only one of the factors or . Thus a pronic number is squarefree if and only if and are also squarefree. The number of distinct prime factors of a pronic number is the sum of the number of distinct prime factors of and .
If 25 is appended to the decimal representation of any pronic number, the result is a square number, the square of a number ending on 5; for example, 625 = 25<sup>2</sup> and 1225 = 35<sup>2</sup>. This is so because
:<math>100n(n+1) + 25 = 100n^2 + 100n + 25 = (10n+5)^2</math>.
The difference between two consecutive unit fractions is the reciprocal of a pronic number:
:<math>\frac{1}{n} - \frac{1}{n+1} = \frac{(n+1) - n}{n(n+1)} = \frac{1}{n(n+1)}</math>