What are the numbers divisible by 401?

401, 802, 1203, 1604, 2005, 2406, 2807, 3208, 3609, 4010, 4411, 4812, 5213, 5614, 6015, 6416, 6817, 7218, 7619, 8020, 8421, 8822, 9223, 9624, 10025, 10426, 10827, 11228, 11629, 12030, 12431, 12832, 13233, 13634, 14035, 14436, 14837, 15238, 15639, 16040, 16441, 16842, 17243, 17644, 18045, 18446, 18847, 19248, 19649, 20050, 20451, 20852, 21253, 21654, 22055, 22456, 22857, 23258, 23659, 24060, 24461, 24862, 25263, 25664, 26065, 26466, 26867, 27268, 27669, 28070, 28471, 28872, 29273, 29674, 30075, 30476, 30877, 31278, 31679, 32080, 32481, 32882, 33283, 33684, 34085, 34486, 34887, 35288, 35689, 36090, 36491, 36892, 37293, 37694, 38095, 38496, 38897, 39298, 39699, 40100, 40501, 40902, 41303, 41704, 42105, 42506, 42907, 43308, 43709, 44110, 44511, 44912, 45313, 45714, 46115, 46516, 46917, 47318, 47719, 48120, 48521, 48922, 49323, 49724, 50125, 50526, 50927, 51328, 51729, 52130, 52531, 52932, 53333, 53734, 54135, 54536, 54937, 55338, 55739, 56140, 56541, 56942, 57343, 57744, 58145, 58546, 58947, 59348, 59749, 60150, 60551, 60952, 61353, 61754, 62155, 62556, 62957, 63358, 63759, 64160, 64561, 64962, 65363, 65764, 66165, 66566, 66967, 67368, 67769, 68170, 68571, 68972, 69373, 69774, 70175, 70576, 70977, 71378, 71779, 72180, 72581, 72982, 73383, 73784, 74185, 74586, 74987, 75388, 75789, 76190, 76591, 76992, 77393, 77794, 78195, 78596, 78997, 79398, 79799, 80200, 80601, 81002, 81403, 81804, 82205, 82606, 83007, 83408, 83809, 84210, 84611, 85012, 85413, 85814, 86215, 86616, 87017, 87418, 87819, 88220, 88621, 89022, 89423, 89824, 90225, 90626, 91027, 91428, 91829, 92230, 92631, 93032, 93433, 93834, 94235, 94636, 95037, 95438, 95839, 96240, 96641, 97042, 97443, 97844, 98245, 98646, 99047, 99448, 99849

There is a total of 249 numbers (up to 100000) that are divisible by 401.
The sum of these numbers is 12481125.
The arithmetic mean of these numbers is 50125.

How to find the numbers divisible by 401?

Finding all the numbers that can be divided by 401 is essentially the same as searching for the multiples of 401: if a number N is a multiple of 401, then 401 is a divisor of N.

Indeed, if we assume that N is a multiple of 401, this means there exists an integer k such that:

$k \times 401 = N$

Conversely, the result of N divided by 401 is this same integer k (without any remainder):

$k = \frac{N}{401}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 401 (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 401 less than 100000):

1 × 401 = 401
2 × 401 = 802
3 × 401 = 1203
...
248 × 401 = 99448
249 × 401 = 99849