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

1,2

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.

Formula

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

Example

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

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 *)

Prog

(Haskell)
a025555 n = a025555_list !! (n-1)
a025555_list = scanl1 lcm $ tail a000217_list
-- Reinhard Zumkeller, Nov 22 2013
(PARI) S=1; for(n=1, 20, S=lcm(S, n*(n+1)/2); print1(S, ", ")) \\ Edward Jiang, Sep 08 2014

Crossrefs

Cf. A051543, A051538.

Sequence in context: A046981 A065943 A275786 * A200925 A140814 A343433

Adjacent sequences: A025552 A025553 A025554 * A025556 A025557 A025558

Keyword

easy,nice,nonn

Author

Clark Kimberling and Asher Auel

Extensions

Corrected by James A. Sellers

Definition rendered more precisely by Reinhard Zumkeller, Nov 22 2013

Status

approved