What are the numbers divisible by 2049?

2049, 4098, 6147, 8196, 10245, 12294, 14343, 16392, 18441, 20490, 22539, 24588, 26637, 28686, 30735, 32784, 34833, 36882, 38931, 40980, 43029, 45078, 47127, 49176, 51225, 53274, 55323, 57372, 59421, 61470, 63519, 65568, 67617, 69666, 71715, 73764, 75813, 77862, 79911, 81960, 84009, 86058, 88107, 90156, 92205, 94254, 96303, 98352

There is a total of 48 numbers (up to 100000) that are divisible by 2049.
The sum of these numbers is 2409624.
The arithmetic mean of these numbers is 50200.5.

How to find the numbers divisible by 2049?

Finding all the numbers that can be divided by 2049 is essentially the same as searching for the multiples of 2049: if a number N is a multiple of 2049, then 2049 is a divisor of N.

Indeed, if we assume that N is a multiple of 2049, this means there exists an integer k such that:

$k \times 2049 = N$

Conversely, the result of N divided by 2049 is this same integer k (without any remainder):

$k = \frac{N}{2049}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 2049 (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 2049 less than 100000):

1 × 2049 = 2049
2 × 2049 = 4098
3 × 2049 = 6147
...
47 × 2049 = 96303
48 × 2049 = 98352