cp's OEIS Frontend

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

%I A002944 M0912 N0344 #79 Dec 25 2023 20:48:15
%S A002944 1,1,2,3,12,10,60,105,280,252,2520,2310,27720,25740,24024,45045,
%T A002944 720720,680680,12252240,11639628,11085360,10581480,232792560,
%U A002944 223092870,1070845776,1029659400,2974571600,2868336900,80313433200,77636318760,2329089562800
%N A002944 a(n) = LCM(1,2,...,n) / n.
%C A002944 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 A002944 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 A002944 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002944 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002944 T. D. Noe, <a href="/A002944/b002944.txt">Table of n, a(n) for n = 1..500</a>
%H A002944 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 A002944 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 A002944 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 A002944 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 A002944 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 A002944 <a href="/index/Lc#lcm">Index entries for sequences related to lcm's</a>
%F A002944 a(n) = A003418(n) / n.
%F A002944 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 A002944 Equally, a(n+1) = LCM_{k=0..n} binomial(n,k). - _Franklin T. Adams-Watters_, Jul 05 2009
%p A002944 A003418 := n-> lcm(seq(i,i=1..n)); f:=n->A003418(n)/n;
%p A002944 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 A002944 Table[Apply[LCM,Range[n]]/n,{n,1,30}]  (* _Geoffrey Critzer_, Feb 10 2013 *)
%o A002944 (PARI) a(n) = lcm(vector(n, i, i))/n; \\ _Michel Marcus_, Apr 16 2014
%o A002944 (Haskell)
%o A002944 a002944 n = a003418 n `div` n  -- _Reinhard Zumkeller_, Mar 16 2015
%Y A002944 Cf. A025527 and A025537.
%Y A002944 Cf. A100561, A003418, A001142, A001405. - _Franklin T. Adams-Watters_, Jul 05 2009
%Y A002944 Cf. A056606 (squarefree kernel).
%K A002944 nonn,easy
%O A002944 1,3
%A A002944 _N. J. A. Sloane_
%E A002944 More terms from _Jud McCranie_, Jan 17 2000
%E A002944 Edited by _N. J. A. Sloane_, Jun 11 2008 and Sep 04 2019