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%I #42 Oct 27 2023 22:00:43
%S 1,3,6,30,30,210,420,1260,1260,13860,13860,180180,180180,180180,
%T 360360,6126120,6126120,116396280,116396280,116396280,116396280,
%U 2677114440,2677114440,13385572200,13385572200,40156716600,40156716600
%N Least common multiple (or LCM) of first n positive triangular numbers (A000217).
%H T. D. Noe, <a href="/A025555/b025555.txt">Table of n, a(n) for n = 1..200</a>
%H Peter Luschny and Stefan Wehmeier, <a href="http://arxiv.org/abs/0909.1838">The lcm(1,2,...,n) as a product of sine values sampled over the points in Farey sequences</a>, arXiv:0909.1838 [math.CA], 2009.
%F a(n) = A003418(n+1)/2. - _Matthew Vandermast_, Jun 04 2012
%e a(5) = lcm{1, 3, 6, 10, 15} = 30.
%p HalfFarey := proc (n) local a,b,c,d,k,s; if n<2 then RETURN([1]) fi; a:=0; b:=1; c:=1; d:=n; s:=NULL; do k := iquo(n+b,d); a,b,c,d := c, d, k*c-a, k*d-b; if b < 2*a then break fi; s := s, a/b od; [s] end:
%p A025555 := proc(n) local r; HalfFarey(n+1); subsop(nops(%) = NULL,%); mul(2*sin(Pi*r),r = %)^2 end: seq(round(evalf(A025555(i))),i=1..27); # _Peter Luschny_, Jun 09 2011
%t nn=30;With[{trnos=Accumulate[Range[nn]]},Table[LCM@@Take[trnos,n], {n,nn}]] (* _Harvey P. Dale_, Oct 21 2011 *)
%t f[x_] := x + 1; a[1] = f[1]; a[n_] := LCM[f[n], a[n - 1]]; Array[a, 30]/2 (* _Robert G. Wilson v_, Jan 04 2013 *)
%o (Haskell)
%o a025555 n = a025555_list !! (n-1)
%o a025555_list = scanl1 lcm $ tail a000217_list
%o -- _Reinhard Zumkeller_, Nov 22 2013
%o (PARI) S=1;for(n=1,20,S=lcm(S,n*(n+1)/2);print1(S,",")) \\ _Edward Jiang_, Sep 08 2014
%Y Cf. A051543, A051538.
%K easy,nice,nonn
%O 1,2
%A _Clark Kimberling_ and _Asher Auel_
%E Corrected by _James A. Sellers_
%E Definition rendered more precisely by _Reinhard Zumkeller_, Nov 22 2013
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