For example, 42 is arithmetic because it has 8 divisors (1, 2, 3, 6, 7, 14, 21, 42) whose average is 96/8 = 12.

All the odd prime numbers are arithmetic. It is possible to find quite long runs of consecutive arithmetic numbers. For example, one of length 105 starts at 3033935561.

Antonio M. Oller-Marcén has proved various properties of arithmetic numbers, for example, that if    is an odd prime then    is arithmetic.

Below, the spiral pattern of arithmetic numbers up to  . See the page on prime numbers for an explanation and links to similar pictures.

The smallest 3 × 3 magic square made of consecutive arithmetic numbers is

The first arithmetic numbers are 1, 3, 5, 6, 7, 11, 13, 14, 15, 17, 19, 20, 21, 22, 23, 27, 29, 30, 31, 33, 35, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 49, 51, 53, 54, 55, 56, 57, 59, 60, 61, 62, 65, 66, 67, 68, 69, 70 more terms

Pictorial representation of remainders (mod 2, 3, ...,11) frequency. For a table of values and more details click here

A graph displaying how many arithmetic numbers are multiples of the primes p from 2 to 71. In black the ideal line 1/p.