The superabundant numbers up to 1015 :
1, 2, 4, 6, 12, 24, 36, 48, 60, 120, 180, 240, 360, 720, 840, 1260, 1680, 2520, 5040, 10080, 15120, 25200, 27720, 55440, 110880, 166320, 277200, 332640, 554400, 665280, 720720, 1441440, 2162160, 3603600, 4324320, 7207200, 8648640, 10810800, 21621600, 36756720, 61261200, 73513440, 122522400, 147026880, 183783600, 367567200, 698377680, 735134400, 1102701600, 1163962800, 1396755360, 2327925600, 2793510720, 3491888400, 6983776800, 13967553600, 20951330400, 27935107200, 41902660800, 48886437600, 80313433200, 160626866400, 321253732800, 481880599200, 642507465600, 963761198400, 1124388064800, 1927522396800, 2248776129600, 3373164194400, 4497552259200, 4658179125600, 6746328388800, 9316358251200, 13974537376800, 18632716502400, 27949074753600, 32607253879200, 55898149507200, 65214507758400, 97821761637600, 130429015516800, 144403552893600, 195643523275200, 288807105787200, 433210658680800, 577614211574400, 866421317361600.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 1000 values, from 1 to 8.74⋅10149).
| n\r | 0 | 1 | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| 2 | 999 | 1 | 2 | ||||||||
| 3 | 997 | 2 | 1 | 3 | |||||||
| 4 | 997 | 1 | 2 | 0 | 4 | ||||||
| 5 | 992 | 3 | 2 | 1 | 2 | 5 | |||||
| 6 | 997 | 1 | 1 | 0 | 1 | 0 | 6 | ||||
| 7 | 986 | 3 | 2 | 2 | 2 | 2 | 3 | 7 | |||
| 8 | 991 | 1 | 1 | 0 | 6 | 0 | 1 | 0 | 8 | ||
| 9 | 988 | 1 | 1 | 4 | 1 | 0 | 5 | 0 | 0 | 9 | |
| 10 | 992 | 1 | 2 | 0 | 2 | 0 | 2 | 0 | 1 | 0 | 10 |
| 11 | 978 | 3 | 3 | 1 | 5 | 2 | 3 | 0 | 2 | 1 | 2 |
A pictorial representation of the table above
Imagine to divide the members of this family by a number n and compute the remainders. Should they be uniformly distributed, each remainder from 0 to n-1 would be obtained in about (1/n)-th of the cases. This outcome is represented by a white square. Reddish (resp. bluish) squares represent remainders which appear more (resp. less) frequently than 1/n.
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