What are the numbers divisible by 3013?

3013, 6026, 9039, 12052, 15065, 18078, 21091, 24104, 27117, 30130, 33143, 36156, 39169, 42182, 45195, 48208, 51221, 54234, 57247, 60260, 63273, 66286, 69299, 72312, 75325, 78338, 81351, 84364, 87377, 90390, 93403, 96416, 99429

There is a total of 33 numbers (up to 100000) that are divisible by 3013.
The sum of these numbers is 1690293.
The arithmetic mean of these numbers is 51221.

How to find the numbers divisible by 3013?

Finding all the numbers that can be divided by 3013 is essentially the same as searching for the multiples of 3013: if a number N is a multiple of 3013, then 3013 is a divisor of N.

Indeed, if we assume that N is a multiple of 3013, this means there exists an integer k such that:

$k \times 3013 = N$

Conversely, the result of N divided by 3013 is this same integer k (without any remainder):

$k = \frac{N}{3013}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 3013 (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 3013 less than 100000):

1 × 3013 = 3013
2 × 3013 = 6026
3 × 3013 = 9039
...
32 × 3013 = 96416
33 × 3013 = 99429