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A083481 Smallest k such that n(n+1)*k is a square. 2


%S 2,6,3,5,30,42,14,2,10,110,33,39,182,210,15,17,34,38,95,105,462,506,

%T 138,6,26,78,21,203,870,930,62,66,1122,1190,35,37,1406,1482,390,410,

%U 1722,1806,473,55,230,2162,141,3,2,102,663,689,318,330,770,798,3306,3422,885

%N Smallest k such that n(n+1)*k is a square.

%C k = p*q*r... is a squarefree number where p,q,r are those prime factors of n(n+1) which have odd index.

%H Harvey P. Dale, <a href="/A083481/b083481.txt">Table of n, a(n) for n = 1..500</a>

%H John M. Campbell, <a href="http://arxiv.org/abs/1105.3399">An Integral Representation of Kekulé Numbers, and Double Integrals Related to Smarandache Sequences</a>, arXiv preprint arXiv:1105.3399 [math.GM], 2011.

%F a(n) = A007913(n*(n+1)). - _R. J. Mathar_, Nov 02 2011

%t sk[n_]:=Module[{k=1},While[!IntegerQ[Sqrt[n*k]],k++];k]; sk/@Table[n(n+1),{n,60}] (* _Harvey P. Dale_, Mar 28 2013 *)

%o (PARI) a(n)=core(n*(n+1))

%Y Cf. A083482.

%K nonn

%O 1,1

%A _Amarnath Murthy_ and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 03 2003

%E More terms from _Benoit Cloitre_, May 04 2003

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Last modified June 19 09:48 EDT 2021. Contains 345126 sequences. (Running on oeis4.)