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A076713 Harshad (Niven) triangular numbers: triangular numbers which are divisible by the sum of their digits. 3
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 (list; graph; refs; listen; history; text; internal format)
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.

Sequence in context: A056411 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

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Last modified September 19 15:31 EDT 2019. Contains 327199 sequences. (Running on oeis4.)