

A081528


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


4



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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 that 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[n1], 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 A180805
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



