What are the numbers divisible by 501?

501, 1002, 1503, 2004, 2505, 3006, 3507, 4008, 4509, 5010, 5511, 6012, 6513, 7014, 7515, 8016, 8517, 9018, 9519, 10020, 10521, 11022, 11523, 12024, 12525, 13026, 13527, 14028, 14529, 15030, 15531, 16032, 16533, 17034, 17535, 18036, 18537, 19038, 19539, 20040, 20541, 21042, 21543, 22044, 22545, 23046, 23547, 24048, 24549, 25050, 25551, 26052, 26553, 27054, 27555, 28056, 28557, 29058, 29559, 30060, 30561, 31062, 31563, 32064, 32565, 33066, 33567, 34068, 34569, 35070, 35571, 36072, 36573, 37074, 37575, 38076, 38577, 39078, 39579, 40080, 40581, 41082, 41583, 42084, 42585, 43086, 43587, 44088, 44589, 45090, 45591, 46092, 46593, 47094, 47595, 48096, 48597, 49098, 49599, 50100, 50601, 51102, 51603, 52104, 52605, 53106, 53607, 54108, 54609, 55110, 55611, 56112, 56613, 57114, 57615, 58116, 58617, 59118, 59619, 60120, 60621, 61122, 61623, 62124, 62625, 63126, 63627, 64128, 64629, 65130, 65631, 66132, 66633, 67134, 67635, 68136, 68637, 69138, 69639, 70140, 70641, 71142, 71643, 72144, 72645, 73146, 73647, 74148, 74649, 75150, 75651, 76152, 76653, 77154, 77655, 78156, 78657, 79158, 79659, 80160, 80661, 81162, 81663, 82164, 82665, 83166, 83667, 84168, 84669, 85170, 85671, 86172, 86673, 87174, 87675, 88176, 88677, 89178, 89679, 90180, 90681, 91182, 91683, 92184, 92685, 93186, 93687, 94188, 94689, 95190, 95691, 96192, 96693, 97194, 97695, 98196, 98697, 99198, 99699

There is a total of 199 numbers (up to 100000) that are divisible by 501.
The sum of these numbers is 9969900.
The arithmetic mean of these numbers is 50100.

How to find the numbers divisible by 501?

Finding all the numbers that can be divided by 501 is essentially the same as searching for the multiples of 501: if a number N is a multiple of 501, then 501 is a divisor of N.

Indeed, if we assume that N is a multiple of 501, this means there exists an integer k such that:

$k \times 501 = N$

Conversely, the result of N divided by 501 is this same integer k (without any remainder):

$k = \frac{N}{501}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 501 (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 501 less than 100000):

1 × 501 = 501
2 × 501 = 1002
3 × 501 = 1503
...
198 × 501 = 99198
199 × 501 = 99699