A081528 a(n) = n*lcm{1,2,...,n}.

1, 4, 18, 48, 300, 360, 2940, 6720, 22680, 25200, 304920, 332640, 4684680, 5045040, 5405400, 11531520, 208288080, 220540320, 4423058640, 4655851200, 4888643760, 5121436320, 123147264240, 128501493120, 669278610000, 696049754400

Offset

1,2

Comments

Denominators in binomial transform of 1/(n + 1)^2. - Paul Barry, Aug 06 2004

Construct a sequence S_n from n sequences b_1, b_2, ..., b_n of periods 1, 2, ..., n, respectively, say, b_1 = [1, 1, ...], b_2 = [1, 2, 1, 2, ...], ..., b_n = [1, 2, 3, ..., n, 1, 2, 3, ..., n, ...], by taking S_n = [b_1(1), b_2(1), ..., b_n(1), b_1(2), b_2(2), ..., b_n(2), ..., b_1(n), b_2(n), ..., b_n(n), ...] (by listing the b_i sequences in rows and taking each column in turn as the next n terms of S_n). Then a(n) is the period of sequence S_n. - Rick L. Shepherd, Aug 21 2006

This is a sequence that goes in strictly ascending order. The related sequence A003418 also goes in ascending order but has consecutive repeated terms. Since n increases, then so too does a(n) even when A003418(n) doesn't. - Alonso del Arte, Nov 25 2012

Links

Table of n, a(n) for n=1..26.

Formula

a(n) = A003418(n) * n. - Martin Fuller, Jan 03 2006

Example

a(2) = 4 because the least common multiple of 1 and 2 is 2, and 2 * 2 = 4.
a(3) = 18 because lcm(1,2,3) = 6, and 3 * 6 = 18.
a(4) = 48 because lcm(1, 2, 3, 4) = 12, and 4 * 12 = 48.

Mathematica

Table[n*LCM@@Range[n], {n, 30}] (* Harvey P. Dale, Oct 09 2012 *)

Prog

(Derive) a(n) := (n + 1)*LCM(VECTOR(k + 1, k, 0, n)) " Paul Barry, Aug 06 2004 "
(PARI) l=vector(35); l[1]=1; print1("1, "); for(n=2, 35, l[n]=lcm(l[n-1], n); print1(n*l[n], ", ")) \\ Rick L. Shepherd, Aug 21 2006

Crossrefs

Cf. A027612, A027611, A022819, A002944, A081530, A097344.

Sequence in context: A073991 A052642 A102928 * A056147 A181857 A353162

Adjacent sequences: A081525 A081526 A081527 * A081529 A081530 A081531

Keyword

nonn,easy

Author

Amarnath Murthy, Mar 27 2003

Extensions

More terms from Paul Barry, Aug 06 2004

Entry revised by N. J. A. Sloane, Jan 15 2006

Status

approved