What are the numbers divisible by 513?

513, 1026, 1539, 2052, 2565, 3078, 3591, 4104, 4617, 5130, 5643, 6156, 6669, 7182, 7695, 8208, 8721, 9234, 9747, 10260, 10773, 11286, 11799, 12312, 12825, 13338, 13851, 14364, 14877, 15390, 15903, 16416, 16929, 17442, 17955, 18468, 18981, 19494, 20007, 20520, 21033, 21546, 22059, 22572, 23085, 23598, 24111, 24624, 25137, 25650, 26163, 26676, 27189, 27702, 28215, 28728, 29241, 29754, 30267, 30780, 31293, 31806, 32319, 32832, 33345, 33858, 34371, 34884, 35397, 35910, 36423, 36936, 37449, 37962, 38475, 38988, 39501, 40014, 40527, 41040, 41553, 42066, 42579, 43092, 43605, 44118, 44631, 45144, 45657, 46170, 46683, 47196, 47709, 48222, 48735, 49248, 49761, 50274, 50787, 51300, 51813, 52326, 52839, 53352, 53865, 54378, 54891, 55404, 55917, 56430, 56943, 57456, 57969, 58482, 58995, 59508, 60021, 60534, 61047, 61560, 62073, 62586, 63099, 63612, 64125, 64638, 65151, 65664, 66177, 66690, 67203, 67716, 68229, 68742, 69255, 69768, 70281, 70794, 71307, 71820, 72333, 72846, 73359, 73872, 74385, 74898, 75411, 75924, 76437, 76950, 77463, 77976, 78489, 79002, 79515, 80028, 80541, 81054, 81567, 82080, 82593, 83106, 83619, 84132, 84645, 85158, 85671, 86184, 86697, 87210, 87723, 88236, 88749, 89262, 89775, 90288, 90801, 91314, 91827, 92340, 92853, 93366, 93879, 94392, 94905, 95418, 95931, 96444, 96957, 97470, 97983, 98496, 99009, 99522

There is a total of 194 numbers (up to 100000) that are divisible by 513.
The sum of these numbers is 9703395.
The arithmetic mean of these numbers is 50017.5.

How to find the numbers divisible by 513?

Finding all the numbers that can be divided by 513 is essentially the same as searching for the multiples of 513: if a number N is a multiple of 513, then 513 is a divisor of N.

Indeed, if we assume that N is a multiple of 513, this means there exists an integer k such that:

$k \times 513 = N$

Conversely, the result of N divided by 513 is this same integer k (without any remainder):

$k = \frac{N}{513}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 513 (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 513 less than 100000):

1 × 513 = 513
2 × 513 = 1026
3 × 513 = 1539
...
193 × 513 = 99009
194 × 513 = 99522