A002944 a(n) = LCM(1,2,...,n) / n.

1, 1, 2, 3, 12, 10, 60, 105, 280, 252, 2520, 2310, 27720, 25740, 24024, 45045, 720720, 680680, 12252240, 11639628, 11085360, 10581480, 232792560, 223092870, 1070845776, 1029659400, 2974571600, 2868336900, 80313433200, 77636318760, 2329089562800

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Equals LCM of all numbers of (n-1)-st row of Pascal's triangle [Montgomery-Breusch]. - J. Lowell, Apr 16 2014. Corrected by N. J. A. Sloane, Sep 04 2019

Williams proves that a(n+1) = A034386(n) for n=2, 11 and 23 only. This is trivially the case for n=0 and 1, too. - Michel Marcus, Apr 16 2020

References

• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• 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..500
• Bakir Farhi, An identity involving the least common multiple of binomial coefficients and its application, arXiv:0906.2295 [math.NT], 2009.
• Bakir Farhi, An identity involving the least common multiple of binomial coefficients and its application, Amer. Math. Monthly, 116 (2009), 836-839.
• Peter L. Montgomery (proposer) and Robert Breusch (solver), LCM of Binomial Coefficients, Problem E2686, American Mathematical Monthly, Vol. 84 (1977), p. 820.
• Peter L. Montgomery (proposer) and Robert Breusch (solver), LCM of Binomial Coefficients, Solution to Problem E2686, American Mathematical Monthly, Vol. 86 (1979), p. 131.
• Ian S. Williams, On a problem of Kurt Mahler concerning binomial coefficents (sic), Bulletin of the Australian Mathematical Society, Volume 14, Issue 2, April 1976, pp. 299-302.
• Index entries for sequences related to lcm's

Crossrefs

Cf. A025527 and A025537.

Cf. A100561, A003418, A001142, A001405. - Franklin T. Adams-Watters, Jul 05 2009

Cf. A056606 (squarefree kernel).

Programs

Haskell

a002944 n = a003418 n `div` n  -- Reinhard Zumkeller, Mar 16 2015

Maple

A003418 := n-> lcm(seq(i,i=1..n)); f:=n->A003418(n)/n;
BB:=n->sum(1/sqrt(k), k=1..n): a:=n->floor(denom(BB(n))/n): seq(a(n), n=1..29); # Zerinvary Lajos, Mar 29 2007

Mathematica

Table[Apply[LCM,Range[n]]/n,{n,1,30}]  (* Geoffrey Critzer, Feb 10 2013 *)

PARI

a(n) = lcm(vector(n, i, i))/n; \\ Michel Marcus, Apr 16 2014

Formula

a(n) = A003418(n) / n.

a(n) = LCM of C(n-1, 0), C(n-1, 1), ..., C(n-1, n-1). [Montgomery-Breusch] [Corrected by N. J. A. Sloane, Jun 11 2008]

Equally, a(n+1) = LCM_{k=0..n} binomial(n,k). - Franklin T. Adams-Watters, Jul 05 2009

Extensions

More terms from Jud McCranie, Jan 17 2000

Edited by N. J. A. Sloane, Jun 11 2008 and Sep 04 2019