What are the numbers divisible by 1026?

1026, 2052, 3078, 4104, 5130, 6156, 7182, 8208, 9234, 10260, 11286, 12312, 13338, 14364, 15390, 16416, 17442, 18468, 19494, 20520, 21546, 22572, 23598, 24624, 25650, 26676, 27702, 28728, 29754, 30780, 31806, 32832, 33858, 34884, 35910, 36936, 37962, 38988, 40014, 41040, 42066, 43092, 44118, 45144, 46170, 47196, 48222, 49248, 50274, 51300, 52326, 53352, 54378, 55404, 56430, 57456, 58482, 59508, 60534, 61560, 62586, 63612, 64638, 65664, 66690, 67716, 68742, 69768, 70794, 71820, 72846, 73872, 74898, 75924, 76950, 77976, 79002, 80028, 81054, 82080, 83106, 84132, 85158, 86184, 87210, 88236, 89262, 90288, 91314, 92340, 93366, 94392, 95418, 96444, 97470, 98496, 99522

There is a total of 97 numbers (up to 100000) that are divisible by 1026.
The sum of these numbers is 4876578.
The arithmetic mean of these numbers is 50274.

How to find the numbers divisible by 1026?

Finding all the numbers that can be divided by 1026 is essentially the same as searching for the multiples of 1026: if a number N is a multiple of 1026, then 1026 is a divisor of N.

Indeed, if we assume that N is a multiple of 1026, this means there exists an integer k such that:

$k \times 1026 = N$

Conversely, the result of N divided by 1026 is this same integer k (without any remainder):

$k = \frac{N}{1026}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 1026 (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 1026 less than 100000):

1 × 1026 = 1026
2 × 1026 = 2052
3 × 1026 = 3078
...
96 × 1026 = 98496
97 × 1026 = 99522