What are the numbers divisible by 3001?

3001, 6002, 9003, 12004, 15005, 18006, 21007, 24008, 27009, 30010, 33011, 36012, 39013, 42014, 45015, 48016, 51017, 54018, 57019, 60020, 63021, 66022, 69023, 72024, 75025, 78026, 81027, 84028, 87029, 90030, 93031, 96032, 99033

There is a total of 33 numbers (up to 100000) that are divisible by 3001.
The sum of these numbers is 1683561.
The arithmetic mean of these numbers is 51017.

How to find the numbers divisible by 3001?

Finding all the numbers that can be divided by 3001 is essentially the same as searching for the multiples of 3001: if a number N is a multiple of 3001, then 3001 is a divisor of N.

Indeed, if we assume that N is a multiple of 3001, this means there exists an integer k such that:

$k \times 3001 = N$

Conversely, the result of N divided by 3001 is this same integer k (without any remainder):

$k = \frac{N}{3001}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 3001 (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 3001 less than 100000):

1 × 3001 = 3001
2 × 3001 = 6002
3 × 3001 = 9003
...
32 × 3001 = 96032
33 × 3001 = 99033