A076713 Harshad (Niven) triangular numbers: triangular numbers which are divisible by the sum of their digits.

1, 3, 6, 10, 21, 36, 45, 120, 153, 171, 190, 210, 300, 351, 378, 465, 630, 666, 780, 820, 990, 1035, 1128, 1275, 1431, 1540, 1596, 1770, 2016, 2080, 2556, 2628, 2850, 2926, 3160, 3240, 3321, 3486, 3570, 4005, 4465, 4560, 4950, 5050, 5460, 5565, 5778, 5886

Offset

1,2

Comments

Intersection of A000217 and A005349. - K. D. Bajpai, Aug 13 2014

Links

K. D. Bajpai, Table of n, a(n) for n = 1..15436

Shyam Sunder Gupta Fascinating Triangular Numbers

Example

a(5)=21: 21 is a triangular number and also a Harshad number as 21 is divisible by 2+1=3. So 21 is Harshad triangular number.

Mathematica

TriangularNumberQ[k_] := If[IntegerQ[1/2 (Sqrt[1 + 8 k] - 1)], True, False]; Harshad[k_] := Select[Range[k], IntegerQ[ #/(Plus @@ IntegerDigits[ # ])] &]; TriangularHarshad[k_] := Select[Harshad[k], TriangularNumberQ[#] &]; TriangularHarshad[5886] (* Ant King, Dec 13 2010 *)
A076713 = {}; Do[k = n*(n + 1)*1/2; If[IntegerQ[k/(Plus @@ IntegerDigits[k])], AppendTo[A076713, k]], {n, 1000}]; A076713  (* K. D. Bajpai, Aug 13 2014 *)

Crossrefs

Cf. A000217, A005349. Includes A037156(n) for n >= 2. Includes A068127.

Sequence in context: A087598 A068855 A068882 * A299017 A136569 A061883

Adjacent sequences: A076710 A076711 A076712 * A076714 A076715 A076716

Keyword

nonn,base

Author

Shyam Sunder Gupta, Oct 26 2002

Status

approved