A069712 Triangular numbers with arithmetic mean of digits = integer (sum of digits = A multiple of the number of digits).

1, 3, 6, 15, 28, 55, 66, 91, 105, 120, 153, 171, 210, 231, 276, 300, 351, 378, 435, 465, 528, 561, 630, 666, 741, 780, 861, 903, 990, 1128, 1326, 1830, 2145, 2415, 3081, 5151, 5995, 6105, 7140, 8385, 8646, 9591, 9870, 10153, 11026, 11175, 12246, 12403

Offset: 0

Author

Amarnath Murthy, Apr 08 2002

Keywords

• base
• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A069709, A069710, A069711.

Programs

Mathematica

Do[ If[ IntegerQ[ Apply[ Plus, IntegerDigits[n(n + 1)/2]] / Floor[ Log[10, n(n + 1)/2] + 1]], Print[n(n + 1)/2]], {n, 1, 10^3}]
Select[Accumulate[Range[200]],IntegerQ[Mean[IntegerDigits[#]]]&] (* Harvey P. Dale, Jun 17 2017 *)

Extensions

Edited and extended by Robert G. Wilson v, Apr 12 2002