A085037 Smallest square divisible by the n-th triangular number (n(n+1)/2).

1, 9, 36, 100, 225, 441, 196, 36, 225, 3025, 4356, 6084, 8281, 11025, 3600, 4624, 2601, 3249, 36100, 44100, 53361, 64009, 19044, 900, 4225, 13689, 15876, 164836, 189225, 216225, 15376, 17424, 314721, 354025, 44100, 49284, 494209, 549081, 152100

Offset: 1

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 19 2003

Keywords

• nonn

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000537, A139131 (square root of this sequence).

Programs

Mathematica

tri = 0; Table[tri = tri + n; {p, e} = Transpose[FactorInteger[tri]]; e = Quotient[(e + 1), 2]; Times @@ (p^(2 e)), {n, 100}] (* T. D. Noe, Aug 01 2011 *)
ssq[n_]:=With[{c=n*Range[1000]},Select[c,IntegerQ[Sqrt[#]]&,1]]; Flatten[ ssq/@Accumulate[Range[40]]] (* Harvey P. Dale, Mar 23 2012 *)

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Jun 25 2003