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 A083481 Smallest k such that n(n+1)*k is a square. 2
 2, 6, 3, 5, 30, 42, 14, 2, 10, 110, 33, 39, 182, 210, 15, 17, 34, 38, 95, 105, 462, 506, 138, 6, 26, 78, 21, 203, 870, 930, 62, 66, 1122, 1190, 35, 37, 1406, 1482, 390, 410, 1722, 1806, 473, 55, 230, 2162, 141, 3, 2, 102, 663, 689, 318, 330, 770, 798, 3306, 3422, 885 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS k = p*q*r... is a squarefree number where p,q,r are those prime factors of n(n+1) which have odd index. LINKS Harvey P. Dale, Table of n, a(n) for n = 1..500 John M. Campbell, An Integral Representation of KekulĂ© Numbers, and Double Integrals Related to Smarandache Sequences, arXiv preprint arXiv:1105.3399 [math.GM], 2011. FORMULA a(n) = A007913(n*(n+1)). - R. J. Mathar, Nov 02 2011 MATHEMATICA 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 *) PROG (PARI) a(n)=core(n*(n+1)) CROSSREFS Cf. A083482. Sequence in context: A323335 A338444 A139384 * A177209 A274439 A280342 Adjacent sequences:  A083478 A083479 A083480 * A083482 A083483 A083484 KEYWORD nonn AUTHOR Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 03 2003 EXTENSIONS More terms from Benoit Cloitre, May 04 2003 STATUS approved

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Last modified May 9 12:48 EDT 2021. Contains 343740 sequences. (Running on oeis4.)