A003102 Largest number divisible by all numbers < its n-th root.

2, 24, 420, 27720, 720720, 36756720, 5354228880, 481880599200, 25619985190800, 10685862914126400, 876240758958364800, 113035057905629059200, 24792356033967973651200, 9690712164777231700912800, 2364533768205644535022723200, 396059406174445459616306136000

Offset: 1

Author

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

Keywords

• nonn
• nice

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

Programs

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,16}] (* T. D. Noe, Aug 01 2006 *)

Formula

It has been shown that a(n) < {p(2n)}^n, where p(2n) is the (2n)-th prime. - Amarnath Murthy, Apr 26 2001

Extensions

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