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

%I #17 Aug 25 2014 12:22:56

%S 1,9,36,100,225,441,196,36,225,3025,4356,6084,8281,11025,3600,4624,

%T 2601,3249,36100,44100,53361,64009,19044,900,4225,13689,15876,164836,

%U 189225,216225,15376,17424,314721,354025,44100,49284,494209,549081,152100

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

%H T. D. Noe, <a href="/A085037/b085037.txt">Table of n, a(n) for n = 1..1000</a>

%t 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 *)

%t ssq[n_]:=With[{c=n*Range[1000]},Select[c,IntegerQ[Sqrt[#]]&,1]]; Flatten[ ssq/@Accumulate[Range[40]]] (* _Harvey P. Dale_, Mar 23 2012 *)

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

%K nonn

%O 1,2

%A _Amarnath Murthy_ and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 19 2003

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

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)