What are the numbers divisible by 2001?

2001, 4002, 6003, 8004, 10005, 12006, 14007, 16008, 18009, 20010, 22011, 24012, 26013, 28014, 30015, 32016, 34017, 36018, 38019, 40020, 42021, 44022, 46023, 48024, 50025, 52026, 54027, 56028, 58029, 60030, 62031, 64032, 66033, 68034, 70035, 72036, 74037, 76038, 78039, 80040, 82041, 84042, 86043, 88044, 90045, 92046, 94047, 96048, 98049

There is a total of 49 numbers (up to 100000) that are divisible by 2001.
The sum of these numbers is 2451225.
The arithmetic mean of these numbers is 50025.

How to find the numbers divisible by 2001?

Finding all the numbers that can be divided by 2001 is essentially the same as searching for the multiples of 2001: if a number N is a multiple of 2001, then 2001 is a divisor of N.

Indeed, if we assume that N is a multiple of 2001, this means there exists an integer k such that:

$k \times 2001 = N$

Conversely, the result of N divided by 2001 is this same integer k (without any remainder):

$k = \frac{N}{2001}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 2001 (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 2001 less than 100000):

1 × 2001 = 2001
2 × 2001 = 4002
3 × 2001 = 6003
...
48 × 2001 = 96048
49 × 2001 = 98049