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

1, 3, 6, 30, 30, 210, 420, 1260, 1260, 13860, 13860, 180180, 180180, 180180, 360360, 6126120, 6126120, 116396280, 116396280, 116396280, 116396280, 2677114440, 2677114440, 13385572200, 13385572200, 40156716600, 40156716600

Offset: 1

Author

Clark Kimberling and Asher Auel

Keywords

• easy
• nice
• nonn

Examples

			a(5) = lcm{1, 3, 6, 10, 15} = 30.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..200
• Peter Luschny and Stefan Wehmeier, The lcm(1,2,...,n) as a product of sine values sampled over the points in Farey sequences, arXiv:0909.1838 [math.CA], 2009.

Crossrefs

Cf. A051543, A051538.

Programs

Haskell

a025555 n = a025555_list !! (n-1)
a025555_list = scanl1 lcm $ tail a000217_list
-- Reinhard Zumkeller, Nov 22 2013

Maple

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:
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

Mathematica

nn=30;With[{trnos=Accumulate[Range[nn]]},Table[LCM@@Take[trnos,n], {n,nn}]] (* Harvey P. Dale, Oct 21 2011 *)
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 *)

PARI

S=1;for(n=1,20,S=lcm(S,n*(n+1)/2);print1(S,",")) \\ Edward Jiang, Sep 08 2014

Formula

a(n) = A003418(n+1)/2. - Matthew Vandermast, Jun 04 2012

Extensions

Corrected by James Sellers

Definition rendered more precisely by Reinhard Zumkeller, Nov 22 2013