A002944 - OEIS

A002944

a(n) = LCM(1,2,...,n) / n.
(Formerly M0912 N0344)

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

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

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

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 *)

PROG

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