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A025555 Least common multiple (or LCM) of first n positive triangular numbers (A000217).

%I A025555 #43 Jul 02 2025 16:01:55
%S A025555 1,3,6,30,30,210,420,1260,1260,13860,13860,180180,180180,180180,
%T A025555 360360,6126120,6126120,116396280,116396280,116396280,116396280,
%U A025555 2677114440,2677114440,13385572200,13385572200,40156716600,40156716600
%N A025555 Least common multiple (or LCM) of first n positive triangular numbers (A000217).
%H A025555 T. D. Noe, <a href="/A025555/b025555.txt">Table of n, a(n) for n = 1..200</a>
%H A025555 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 A025555 a(n) = A003418(n+1)/2. - _Matthew Vandermast_, Jun 04 2012
%e A025555 a(5) = lcm{1, 3, 6, 10, 15} = 30.
%p A025555 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 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 A025555 nn=30;With[{trnos=Accumulate[Range[nn]]},Table[LCM@@Take[trnos,n], {n,nn}]] (* _Harvey P. Dale_, Oct 21 2011 *)
%t A025555 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 A025555 (Haskell)
%o A025555 a025555 n = a025555_list !! (n-1)
%o A025555 a025555_list = scanl1 lcm $ tail a000217_list
%o A025555 -- _Reinhard Zumkeller_, Nov 22 2013
%o A025555 (PARI) S=1;for(n=1,20,S=lcm(S,n*(n+1)/2);print1(S,",")) \\ _Edward Jiang_, Sep 08 2014
%Y A025555 Cf. A051543, A051538.
%K A025555 easy,nice,nonn
%O A025555 1,2
%A A025555 _Clark Kimberling_ and _Asher Auel_
%E A025555 Corrected by _James Sellers_
%E A025555 Definition rendered more precisely by _Reinhard Zumkeller_, Nov 22 2013