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

Offset

1,1

References

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.

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

Henry W. Gould, Letters to N. J. A. Sloane, Oct 1973 and Jan 1974.

A. Murthy, Some New Smarandache Sequences, Functions and Partitions, Smarandache Notions Journal, Vol. 11, No. 1-2-3, Spring 2000, p. 179.

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 ]. [Annotated scanned copy]

D. L. Silverman, Problem 159, Pi Mu Epsilon Journal, Vol. 4, No. 3, Fall 1965, p. 124.

D. L. Silverman, Problem 159, Pi Mu Epsilon Journal, Vol. 4, No. 3, Fall 1965, p. 124. [Annotated scanned copy]

Smarandache web site

Formula

It has been shown that a(n) < {p(2n)}^n, where p(2n) is the (2n)-th prime. - Amarnath Murthy, 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[(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

Crossrefs

Sequence in context: A219431 A214688 A364195 * A370847 A304318 A337505

Adjacent sequences: A003099 A003100 A003101 * A003103 A003104 A003105

Keyword

nonn,nice

Author

N. J. A. Sloane, H. W. Gould

Extensions

Corrected and extended by T. D. Noe, Aug 01 2006

Status

approved