What are the numbers divisible by 506?

506, 1012, 1518, 2024, 2530, 3036, 3542, 4048, 4554, 5060, 5566, 6072, 6578, 7084, 7590, 8096, 8602, 9108, 9614, 10120, 10626, 11132, 11638, 12144, 12650, 13156, 13662, 14168, 14674, 15180, 15686, 16192, 16698, 17204, 17710, 18216, 18722, 19228, 19734, 20240, 20746, 21252, 21758, 22264, 22770, 23276, 23782, 24288, 24794, 25300, 25806, 26312, 26818, 27324, 27830, 28336, 28842, 29348, 29854, 30360, 30866, 31372, 31878, 32384, 32890, 33396, 33902, 34408, 34914, 35420, 35926, 36432, 36938, 37444, 37950, 38456, 38962, 39468, 39974, 40480, 40986, 41492, 41998, 42504, 43010, 43516, 44022, 44528, 45034, 45540, 46046, 46552, 47058, 47564, 48070, 48576, 49082, 49588, 50094, 50600, 51106, 51612, 52118, 52624, 53130, 53636, 54142, 54648, 55154, 55660, 56166, 56672, 57178, 57684, 58190, 58696, 59202, 59708, 60214, 60720, 61226, 61732, 62238, 62744, 63250, 63756, 64262, 64768, 65274, 65780, 66286, 66792, 67298, 67804, 68310, 68816, 69322, 69828, 70334, 70840, 71346, 71852, 72358, 72864, 73370, 73876, 74382, 74888, 75394, 75900, 76406, 76912, 77418, 77924, 78430, 78936, 79442, 79948, 80454, 80960, 81466, 81972, 82478, 82984, 83490, 83996, 84502, 85008, 85514, 86020, 86526, 87032, 87538, 88044, 88550, 89056, 89562, 90068, 90574, 91080, 91586, 92092, 92598, 93104, 93610, 94116, 94622, 95128, 95634, 96140, 96646, 97152, 97658, 98164, 98670, 99176, 99682

There is a total of 197 numbers (up to 100000) that are divisible by 506.
The sum of these numbers is 9868518.
The arithmetic mean of these numbers is 50094.

How to find the numbers divisible by 506?

Finding all the numbers that can be divided by 506 is essentially the same as searching for the multiples of 506: if a number N is a multiple of 506, then 506 is a divisor of N.

Indeed, if we assume that N is a multiple of 506, this means there exists an integer k such that:

$k \times 506 = N$

Conversely, the result of N divided by 506 is this same integer k (without any remainder):

$k = \frac{N}{506}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 506 (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 506 less than 100000):

1 × 506 = 506
2 × 506 = 1012
3 × 506 = 1518
...
196 × 506 = 99176
197 × 506 = 99682