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A025555 Least common multiple (or LCM) of first n positive triangular numbers (A000217). 6
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 (list; graph; refs; listen; history; text; internal format)
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

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 (asher.auel(AT)reed.edu)

EXTENSIONS

Corrected by James A. Sellers

Definition rendered more precisely by Reinhard Zumkeller, Nov 22 2013

STATUS

approved

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Last modified September 18 15:58 EDT 2021. Contains 347527 sequences. (Running on oeis4.)