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A076713
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Harshad (Niven) triangular numbers: triangular numbers which are divisible by the sum of their digits.
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3
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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
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OFFSET
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1,2
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COMMENTS
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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