What are the numbers divisible by 1023?

1023, 2046, 3069, 4092, 5115, 6138, 7161, 8184, 9207, 10230, 11253, 12276, 13299, 14322, 15345, 16368, 17391, 18414, 19437, 20460, 21483, 22506, 23529, 24552, 25575, 26598, 27621, 28644, 29667, 30690, 31713, 32736, 33759, 34782, 35805, 36828, 37851, 38874, 39897, 40920, 41943, 42966, 43989, 45012, 46035, 47058, 48081, 49104, 50127, 51150, 52173, 53196, 54219, 55242, 56265, 57288, 58311, 59334, 60357, 61380, 62403, 63426, 64449, 65472, 66495, 67518, 68541, 69564, 70587, 71610, 72633, 73656, 74679, 75702, 76725, 77748, 78771, 79794, 80817, 81840, 82863, 83886, 84909, 85932, 86955, 87978, 89001, 90024, 91047, 92070, 93093, 94116, 95139, 96162, 97185, 98208, 99231

There is a total of 97 numbers (up to 100000) that are divisible by 1023.
The sum of these numbers is 4862319.
The arithmetic mean of these numbers is 50127.

How to find the numbers divisible by 1023?

Finding all the numbers that can be divided by 1023 is essentially the same as searching for the multiples of 1023: if a number N is a multiple of 1023, then 1023 is a divisor of N.

Indeed, if we assume that N is a multiple of 1023, this means there exists an integer k such that:

$k \times 1023 = N$

Conversely, the result of N divided by 1023 is this same integer k (without any remainder):

$k = \frac{N}{1023}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 1023 (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 1023 less than 100000):

1 × 1023 = 1023
2 × 1023 = 2046
3 × 1023 = 3069
...
96 × 1023 = 98208
97 × 1023 = 99231