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A002944 LCM{1,2,...,n} / n.
(Formerly M0912 N0344)
25
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

Conjecture: LCM of all numbers of n-th row of Pascal's triangle. - J. Lowell, Apr 16 2014

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.

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, LCM of Binomial Coefficients, Problem E2686, American Mathematical Monthly, Vol. 84 (1977), p. 820.

Peter L. Montgomery, LCM of Binomial Coefficients, Solution to Problem E2686, American Mathematical Monthly, Vol. 86 (1979), p. 131.

Index entries for sequences related to lcm's

FORMULA

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

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

a(n+1) = lcm( C(n,k), k=0..n). - 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

(Haskell)

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

CROSSREFS

Cf. A025527.

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

Cf. A056606 (squarefree kernel).

Sequence in context: A212303 A100561 A081529 * A266366 A201501 A037321

Adjacent sequences:  A002941 A002942 A002943 * A002945 A002946 A002947

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Jud McCranie, Jan 17 2000

Edited by N. J. A. Sloane, Jun 11 2008

STATUS

approved

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Last modified June 29 01:52 EDT 2017. Contains 288857 sequences.