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A002944 a(n) = LCM(1,2,...,n) / n.
(Formerly M0912 N0344)
34

%I M0912 N0344 #79 Dec 25 2023 20:48:15

%S 1,1,2,3,12,10,60,105,280,252,2520,2310,27720,25740,24024,45045,

%T 720720,680680,12252240,11639628,11085360,10581480,232792560,

%U 223092870,1070845776,1029659400,2974571600,2868336900,80313433200,77636318760,2329089562800

%N a(n) = LCM(1,2,...,n) / n.

%C 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

%C 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

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H T. D. Noe, <a href="/A002944/b002944.txt">Table of n, a(n) for n = 1..500</a>

%H Bakir Farhi, <a href="http://arxiv.org/abs/0906.2295">An identity involving the least common multiple of binomial coefficients and its application</a>, arXiv:0906.2295 [math.NT], 2009.

%H Bakir Farhi, <a href="http://www.jstor.org/stable/40391302">An identity involving the least common multiple of binomial coefficients and its application</a>, Amer. Math. Monthly, 116 (2009), 836-839.

%H Peter L. Montgomery (proposer) and Robert Breusch (solver), <a href="http://www.jstor.org/stable/2322067">LCM of Binomial Coefficients, Problem E2686</a>, American Mathematical Monthly, Vol. 84 (1977), p. 820.

%H Peter L. Montgomery (proposer) and Robert Breusch (solver), <a href="http://www.jstor.org/stable/2321959">LCM of Binomial Coefficients, Solution to Problem E2686</a>, American Mathematical Monthly, Vol. 86 (1979), p. 131.

%H Ian S. Williams, <a href="https://doi.org/10.1017/S0004972700025120">On a problem of Kurt Mahler concerning binomial coefficents</a> (sic), Bulletin of the Australian Mathematical Society, Volume 14, Issue 2, April 1976, pp. 299-302.

%H <a href="/index/Lc#lcm">Index entries for sequences related to lcm's</a>

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

%F 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]

%F Equally, a(n+1) = LCM_{k=0..n} binomial(n,k). - _Franklin T. Adams-Watters_, Jul 05 2009

%p A003418 := n-> lcm(seq(i,i=1..n)); f:=n->A003418(n)/n;

%p 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

%t Table[Apply[LCM,Range[n]]/n,{n,1,30}] (* _Geoffrey Critzer_, Feb 10 2013 *)

%o (PARI) a(n) = lcm(vector(n, i, i))/n; \\ _Michel Marcus_, Apr 16 2014

%o (Haskell)

%o a002944 n = a003418 n `div` n -- _Reinhard Zumkeller_, Mar 16 2015

%Y Cf. A025527 and A025537.

%Y Cf. A100561, A003418, A001142, A001405. - _Franklin T. Adams-Watters_, Jul 05 2009

%Y Cf. A056606 (squarefree kernel).

%K nonn,easy

%O 1,3

%A _N. J. A. Sloane_

%E More terms from _Jud McCranie_, Jan 17 2000

%E Edited by _N. J. A. Sloane_, Jun 11 2008 and Sep 04 2019

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)