What are the numbers divisible by 1006?

1006, 2012, 3018, 4024, 5030, 6036, 7042, 8048, 9054, 10060, 11066, 12072, 13078, 14084, 15090, 16096, 17102, 18108, 19114, 20120, 21126, 22132, 23138, 24144, 25150, 26156, 27162, 28168, 29174, 30180, 31186, 32192, 33198, 34204, 35210, 36216, 37222, 38228, 39234, 40240, 41246, 42252, 43258, 44264, 45270, 46276, 47282, 48288, 49294, 50300, 51306, 52312, 53318, 54324, 55330, 56336, 57342, 58348, 59354, 60360, 61366, 62372, 63378, 64384, 65390, 66396, 67402, 68408, 69414, 70420, 71426, 72432, 73438, 74444, 75450, 76456, 77462, 78468, 79474, 80480, 81486, 82492, 83498, 84504, 85510, 86516, 87522, 88528, 89534, 90540, 91546, 92552, 93558, 94564, 95570, 96576, 97582, 98588, 99594

There is a total of 99 numbers (up to 100000) that are divisible by 1006.
The sum of these numbers is 4979700.
The arithmetic mean of these numbers is 50300.

How to find the numbers divisible by 1006?

Finding all the numbers that can be divided by 1006 is essentially the same as searching for the multiples of 1006: if a number N is a multiple of 1006, then 1006 is a divisor of N.

Indeed, if we assume that N is a multiple of 1006, this means there exists an integer k such that:

$k \times 1006 = N$

Conversely, the result of N divided by 1006 is this same integer k (without any remainder):

$k = \frac{N}{1006}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 1006 (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 1006 less than 100000):

1 × 1006 = 1006
2 × 1006 = 2012
3 × 1006 = 3018
...
98 × 1006 = 98588
99 × 1006 = 99594