What are the numbers divisible by 465?

465, 930, 1395, 1860, 2325, 2790, 3255, 3720, 4185, 4650, 5115, 5580, 6045, 6510, 6975, 7440, 7905, 8370, 8835, 9300, 9765, 10230, 10695, 11160, 11625, 12090, 12555, 13020, 13485, 13950, 14415, 14880, 15345, 15810, 16275, 16740, 17205, 17670, 18135, 18600, 19065, 19530, 19995, 20460, 20925, 21390, 21855, 22320, 22785, 23250, 23715, 24180, 24645, 25110, 25575, 26040, 26505, 26970, 27435, 27900, 28365, 28830, 29295, 29760, 30225, 30690, 31155, 31620, 32085, 32550, 33015, 33480, 33945, 34410, 34875, 35340, 35805, 36270, 36735, 37200, 37665, 38130, 38595, 39060, 39525, 39990, 40455, 40920, 41385, 41850, 42315, 42780, 43245, 43710, 44175, 44640, 45105, 45570, 46035, 46500, 46965, 47430, 47895, 48360, 48825, 49290, 49755, 50220, 50685, 51150, 51615, 52080, 52545, 53010, 53475, 53940, 54405, 54870, 55335, 55800, 56265, 56730, 57195, 57660, 58125, 58590, 59055, 59520, 59985, 60450, 60915, 61380, 61845, 62310, 62775, 63240, 63705, 64170, 64635, 65100, 65565, 66030, 66495, 66960, 67425, 67890, 68355, 68820, 69285, 69750, 70215, 70680, 71145, 71610, 72075, 72540, 73005, 73470, 73935, 74400, 74865, 75330, 75795, 76260, 76725, 77190, 77655, 78120, 78585, 79050, 79515, 79980, 80445, 80910, 81375, 81840, 82305, 82770, 83235, 83700, 84165, 84630, 85095, 85560, 86025, 86490, 86955, 87420, 87885, 88350, 88815, 89280, 89745, 90210, 90675, 91140, 91605, 92070, 92535, 93000, 93465, 93930, 94395, 94860, 95325, 95790, 96255, 96720, 97185, 97650, 98115, 98580, 99045, 99510, 99975

There is a total of 215 numbers (up to 100000) that are divisible by 465.
The sum of these numbers is 10797300.
The arithmetic mean of these numbers is 50220.

How to find the numbers divisible by 465?

Finding all the numbers that can be divided by 465 is essentially the same as searching for the multiples of 465: if a number N is a multiple of 465, then 465 is a divisor of N.

Indeed, if we assume that N is a multiple of 465, this means there exists an integer k such that:

$k \times 465 = N$

Conversely, the result of N divided by 465 is this same integer k (without any remainder):

$k = \frac{N}{465}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 465 (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 465 less than 100000):

1 × 465 = 465
2 × 465 = 930
3 × 465 = 1395
...
214 × 465 = 99510
215 × 465 = 99975