Pronic number

A pronic number is a number which is the product of 2 successive integers. It can be expressed as this:

$$P_n=n(n+1)=2T_n=\sum_{i=1}^n{2i}=2+4+...+(n-2)+n$$

It is also known as a rectangular number, an oblong number and a rectangle number.

Being a product of 2 consecutive whole numbers, pronic numbers are always even numbers.

Mathematical properties
Pronic numbers are even numbers. Therefore, all pronic numbers but 2 are composite numbers since they are multiples of 2. There are two reasons. There are no odd pronic number but there is a prime pronic number: the only even prime, 2.
 * 1) If $$i(i+1)=n$$, either i or (i + 1) has to be an even number. Since an even number multiplied by any integer is still an even number, pronic numbers are even.
 * 2) Pronic numbers are twice of triangular numbers. The picture showing 12 is actually 2 &times; (3 + 2 + 1).

The only pronic triangular number, 6, is the only perfect number to be a pronic number. The rest are just triangular.

Example
240 is a pronic number. As 240 is equal to 15 &times; 16, it is a pronic number.

It is also related to the triangular number 120.

List of pronic numbers to 1000
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

Bold = Abundant pronic number