A003102 - OEIS

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A003102

Largest number divisible by all numbers < its n-th root.
(Formerly M2139)

2, 24, 420, 27720, 720720, 36756720, 5354228880, 481880599200, 25619985190800, 10685862914126400, 876240758958364800, 113035057905629059200, 24792356033967973651200, 9690712164777231700912800, 2364533768205644535022723200, 396059406174445459616306136000 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,1`
	REFERENCES	`A. Murthy, Some New Smarandache Sequence, Functions and Partitions, Smarandache Notions Journal, Vol. 11, No. 1-2-3, Spring 2000.` `A. Murthy, An application of Smarandache LCM sequence and the largest number divisible by all the integers not exceeding the r-th root, Preprint.` `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 ].` `J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 277.` `D. O. Shklyarsky, N. N. Chentsov and I. M. Yaglom, Selected Problems and Theorems in Elementary Mathematics; Problem 78; Mir Publishers, Moscow.` `D. L. Silverman, Problem 159, Pi Mu Epsilon Journal, Vol. 4, No. 3, Fall 1965, p. 124.` `N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).`
	LINKS	`T. D. Noe, Table of n, a(n) for n = 1..50` `Smarandache web site`
	FORMULA	`It has been shown that a(n) < {p(2n)}^n, where p(2n) is the (2n)-th prime. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Apr 26 2001`
	MATHEMATICA	`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[(mgood)^(1/n)]; Union[Mod[mgood, Range[r]]]=={0}, m++ ]; m=m-1; m*good, {n, 50}] - T. D. Noe (noe(AT)sspectra.com), Aug 01 2006`
	CROSSREFS	`Sequence in context: A052670 A052736 A103904 * A052712 A133413 A012236` `Adjacent sequences: A003099 A003100 A003101 * A003103 A003104 A003105`
	KEYWORD	`nonn,nice`
	AUTHOR	`N. J. A. Sloane (njas(AT)research.att.com), H. W. Gould`
	EXTENSIONS	`Corrected and extended by T. D. Noe (noe(AT)sspectra.com), Aug 01 2006`

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Last modified February 14 02:58 EST 2012. Contains 205567 sequences.