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%I M2139 #25 Jun 14 2017 19:19:58
%S 2,24,420,27720,720720,36756720,5354228880,481880599200,
%T 25619985190800,10685862914126400,876240758958364800,
%U 113035057905629059200,24792356033967973651200,9690712164777231700912800,2364533768205644535022723200,396059406174445459616306136000
%N Largest number divisible by all numbers < its n-th root.
%D A. Murthy, An application of Smarandache LCM sequence and the largest number divisible by all the integers not exceeding the r-th root, Preprint.
%D N. Ozeki, On the problem 1, 2, 3, ..., [ n^(1/k) ] | n, Journal of the College of Arts and Sciences, Chiba University (Chiba, Japan), Vol. 3, No. 4 (Sept. 1962), pp. 427-431 [ Math. Rev. 30 213(1085) 1965 ].
%D J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 277.
%D D. O. Shklyarsky, N. N. Chentsov and I. M. Yaglom, Selected Problems and Theorems in Elementary Mathematics; Problem 78; Mir Publishers, Moscow.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H T. D. Noe, <a href="/A003102/b003102.txt">Table of n, a(n) for n = 1..50</a>
%H Henry W. Gould, <a href="/A003099/a003099.pdf">Letters to N. J. A. Sloane, Oct 1973 and Jan 1974</a>.
%H A. Murthy, <a href="http://fs.gallup.unm.edu/SNJ11.pdf">Some New Smarandache Sequences, Functions and Partitions</a>, Smarandache Notions Journal, Vol. 11, No. 1-2-3, Spring 2000, p. 179.
%H N. Ozeki, <a href="/A003102/a003102.pdf">On the problem 1, 2, 3, ..., [ n^(1/k) ] | n</a>, Journal of the College of Arts and Sciences, Chiba University (Chiba, Japan), Vol. 3, No. 4 (Sept. 1962), pp. 427-431 [ Math. Rev. 30 213(1085) 1965 ]. [Annotated scanned copy]
%H D. L. Silverman, <a href="http://www.pme-math.org/journal/issues/PMEJ.Vol.4.No.3.pdf">Problem 159</a>, Pi Mu Epsilon Journal, Vol. 4, No. 3, Fall 1965, p. 124.
%H D. L. Silverman, <a href="/A003102/a003102_1.pdf">Problem 159</a>, Pi Mu Epsilon Journal, Vol. 4, No. 3, Fall 1965, p. 124. [Annotated scanned copy]
%H <a href="http://www.gallup.unm.edu/~smarandache">Smarandache web site</a>
%F It has been shown that a(n) < {p(2n)}^n, where p(2n) is the (2n)-th prime. - _Amarnath Murthy_, Apr 26 2001
%t k=1; lc=1; Table[While[r=Floor[lc^(1/n)]; Union[Mod[lc,Range[r]]]=={0}, k++; good=lc; lc=LCM[lc,k]]; m=2; While[r=Floor[(m*good)^(1/n)]; Union[Mod[m*good,Range[r]]]=={0}, m++ ]; m=m-1; m*good, {n,50}] - _T. D. Noe_, Aug 01 2006
%K nonn,nice
%O 1,1
%A _N. J. A. Sloane_, H. W. Gould
%E Corrected and extended by _T. D. Noe_, Aug 01 2006
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