What are the numbers divisible by 4009?

4009, 8018, 12027, 16036, 20045, 24054, 28063, 32072, 36081, 40090, 44099, 48108, 52117, 56126, 60135, 64144, 68153, 72162, 76171, 80180, 84189, 88198, 92207, 96216

There is a total of 24 numbers (up to 100000) that are divisible by 4009.
The sum of these numbers is 1202700.
The arithmetic mean of these numbers is 50112.5.

How to find the numbers divisible by 4009?

Finding all the numbers that can be divided by 4009 is essentially the same as searching for the multiples of 4009: if a number N is a multiple of 4009, then 4009 is a divisor of N.

Indeed, if we assume that N is a multiple of 4009, this means there exists an integer k such that:

$k \times 4009 = N$

Conversely, the result of N divided by 4009 is this same integer k (without any remainder):

$k = \frac{N}{4009}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 4009 (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 4009 less than 100000):

1 × 4009 = 4009
2 × 4009 = 8018
3 × 4009 = 12027
...
23 × 4009 = 92207
24 × 4009 = 96216