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triangular numbers
Figurate numbers of the form n(n+1)/2. more

The first 600 triangular numbers :

Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 44721359 values, from 1 to 999999997764120).

n\r 0  1
22236067922360680 2
329814239149071200 3
411180339111803401118034011180340 4
51788854317888544089442720 5
614907119745356001490712074535600 6
71277753012777531012777532006388766 7
855901695590170559017055901705590170559017055901705590170 8
99938079149071200993808000993808000 9
108944271894427204472136089442728944272044721360 10
1181311568131157081311564065578081311560008131156

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.