What are the numbers divisible by 1059?

1059, 2118, 3177, 4236, 5295, 6354, 7413, 8472, 9531, 10590, 11649, 12708, 13767, 14826, 15885, 16944, 18003, 19062, 20121, 21180, 22239, 23298, 24357, 25416, 26475, 27534, 28593, 29652, 30711, 31770, 32829, 33888, 34947, 36006, 37065, 38124, 39183, 40242, 41301, 42360, 43419, 44478, 45537, 46596, 47655, 48714, 49773, 50832, 51891, 52950, 54009, 55068, 56127, 57186, 58245, 59304, 60363, 61422, 62481, 63540, 64599, 65658, 66717, 67776, 68835, 69894, 70953, 72012, 73071, 74130, 75189, 76248, 77307, 78366, 79425, 80484, 81543, 82602, 83661, 84720, 85779, 86838, 87897, 88956, 90015, 91074, 92133, 93192, 94251, 95310, 96369, 97428, 98487, 99546

There is a total of 94 numbers (up to 100000) that are divisible by 1059.
The sum of these numbers is 4728435.
The arithmetic mean of these numbers is 50302.5.

How to find the numbers divisible by 1059?

Finding all the numbers that can be divided by 1059 is essentially the same as searching for the multiples of 1059: if a number N is a multiple of 1059, then 1059 is a divisor of N.

Indeed, if we assume that N is a multiple of 1059, this means there exists an integer k such that:

$k \times 1059 = N$

Conversely, the result of N divided by 1059 is this same integer k (without any remainder):

$k = \frac{N}{1059}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 1059 (we can keep multiplying it by increasingly larger integers, without ever reaching the end).

However, in this instance, we've chosen to set an arbitrary limit (specifically, the multiples of 1059 less than 100000):

1 × 1059 = 1059
2 × 1059 = 2118
3 × 1059 = 3177
...
93 × 1059 = 98487
94 × 1059 = 99546