What are the numbers divisible by 729?

729, 1458, 2187, 2916, 3645, 4374, 5103, 5832, 6561, 7290, 8019, 8748, 9477, 10206, 10935, 11664, 12393, 13122, 13851, 14580, 15309, 16038, 16767, 17496, 18225, 18954, 19683, 20412, 21141, 21870, 22599, 23328, 24057, 24786, 25515, 26244, 26973, 27702, 28431, 29160, 29889, 30618, 31347, 32076, 32805, 33534, 34263, 34992, 35721, 36450, 37179, 37908, 38637, 39366, 40095, 40824, 41553, 42282, 43011, 43740, 44469, 45198, 45927, 46656, 47385, 48114, 48843, 49572, 50301, 51030, 51759, 52488, 53217, 53946, 54675, 55404, 56133, 56862, 57591, 58320, 59049, 59778, 60507, 61236, 61965, 62694, 63423, 64152, 64881, 65610, 66339, 67068, 67797, 68526, 69255, 69984, 70713, 71442, 72171, 72900, 73629, 74358, 75087, 75816, 76545, 77274, 78003, 78732, 79461, 80190, 80919, 81648, 82377, 83106, 83835, 84564, 85293, 86022, 86751, 87480, 88209, 88938, 89667, 90396, 91125, 91854, 92583, 93312, 94041, 94770, 95499, 96228, 96957, 97686, 98415, 99144, 99873

There is a total of 137 numbers (up to 100000) that are divisible by 729.
The sum of these numbers is 6891237.
The arithmetic mean of these numbers is 50301.

How to find the numbers divisible by 729?

Finding all the numbers that can be divided by 729 is essentially the same as searching for the multiples of 729: if a number N is a multiple of 729, then 729 is a divisor of N.

Indeed, if we assume that N is a multiple of 729, this means there exists an integer k such that:

$k \times 729 = N$

Conversely, the result of N divided by 729 is this same integer k (without any remainder):

$k = \frac{N}{729}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 729 (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 729 less than 100000):

1 × 729 = 729
2 × 729 = 1458
3 × 729 = 2187
...
136 × 729 = 99144
137 × 729 = 99873