What are the numbers divisible by 509?

509, 1018, 1527, 2036, 2545, 3054, 3563, 4072, 4581, 5090, 5599, 6108, 6617, 7126, 7635, 8144, 8653, 9162, 9671, 10180, 10689, 11198, 11707, 12216, 12725, 13234, 13743, 14252, 14761, 15270, 15779, 16288, 16797, 17306, 17815, 18324, 18833, 19342, 19851, 20360, 20869, 21378, 21887, 22396, 22905, 23414, 23923, 24432, 24941, 25450, 25959, 26468, 26977, 27486, 27995, 28504, 29013, 29522, 30031, 30540, 31049, 31558, 32067, 32576, 33085, 33594, 34103, 34612, 35121, 35630, 36139, 36648, 37157, 37666, 38175, 38684, 39193, 39702, 40211, 40720, 41229, 41738, 42247, 42756, 43265, 43774, 44283, 44792, 45301, 45810, 46319, 46828, 47337, 47846, 48355, 48864, 49373, 49882, 50391, 50900, 51409, 51918, 52427, 52936, 53445, 53954, 54463, 54972, 55481, 55990, 56499, 57008, 57517, 58026, 58535, 59044, 59553, 60062, 60571, 61080, 61589, 62098, 62607, 63116, 63625, 64134, 64643, 65152, 65661, 66170, 66679, 67188, 67697, 68206, 68715, 69224, 69733, 70242, 70751, 71260, 71769, 72278, 72787, 73296, 73805, 74314, 74823, 75332, 75841, 76350, 76859, 77368, 77877, 78386, 78895, 79404, 79913, 80422, 80931, 81440, 81949, 82458, 82967, 83476, 83985, 84494, 85003, 85512, 86021, 86530, 87039, 87548, 88057, 88566, 89075, 89584, 90093, 90602, 91111, 91620, 92129, 92638, 93147, 93656, 94165, 94674, 95183, 95692, 96201, 96710, 97219, 97728, 98237, 98746, 99255, 99764

There is a total of 196 numbers (up to 100000) that are divisible by 509.
The sum of these numbers is 9826754.
The arithmetic mean of these numbers is 50136.5.

How to find the numbers divisible by 509?

Finding all the numbers that can be divided by 509 is essentially the same as searching for the multiples of 509: if a number N is a multiple of 509, then 509 is a divisor of N.

Indeed, if we assume that N is a multiple of 509, this means there exists an integer k such that:

$k \times 509 = N$

Conversely, the result of N divided by 509 is this same integer k (without any remainder):

$k = \frac{N}{509}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 509 (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 509 less than 100000):

1 × 509 = 509
2 × 509 = 1018
3 × 509 = 1527
...
195 × 509 = 99255
196 × 509 = 99764