0,3

Product over all primes of highest power of prime less than or equal to n. a(0) = 1 by convention.

Also smallest number such that its set of divisors contains an n-term arithmetic progression. - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Dec 09 2002

The prime number theorem implies that LCM(1,2,...,n) = e^(n(1+o(1))) as n -> infinity. In other words, ln(LCM(1,2,...,n))/n -> 1 as n -> infinity. - Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Jan 17 2005

An assertion equivalent to the Riemann hypothesis is: | ln(a(n)) - n | < sqrt(n)*(ln(n))^2. - Lekraj Beedassy (blekraj(AT)yahoo.com), Aug 27 2006

Row products of A133233. - Mats Granvik (mgranvik(AT)abo.fi), Jan 22 2008

J. M. Borwein and P. B. Borwein, Pi and the AGM, Wiley, 1987, p. 365.

Selmer, Ernst S.; On the number of prime divisors of a binomial coefficient. Math. Scand. 39 (1976), no. 2, 271-281 (1977).

J. Sondow, Criteria for irrationality of Euler's constant, Proc. Amer. Math. Soc. 131 (2003) 3335-3344.

T. D. Noe, Table of n, a(n) for n = 0..500

J. Sondow, Criteria for irrationality of Euler's constant

Eric Weisstein's World of Mathematics, Least Common Multiple

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

D. Williams, LCM

Index entries for sequences related to lcm's

Index entries for "core" sequences

a(n)=product_{p^(floor(log n/log p))}, where p runs through primes not exceeding n (i.e. primes 2 through A007917(n)). - Lekraj Beedassy (blekraj(AT)yahoo.com), Jul 27 2004

LCM of {1,2,3,4,5,6} = 60.

A003418 := n-> lcm(seq(i, i=1..n));

seq (denom(sum((-1)^i/i, i = 1..n)), n=0..30); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 14 2008

Table[LCM @@ Range[n], {n, 1, 40}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 01 2006

(PARI) a(n)=local(t); t=n>=0; forprime(p=2, n, t*=p^(log(n)\log(p))); t

(PARI) a(n)=if(n<1, n==0, 1/content(vector(n, k, 1/k)))

Cf. A002944, A102910, A093880, A133233.

a(n) = A079542(n+1,2) for n>1.

It appears that A020500(n) = A003418(n+1)/a(n) - Asher Auel (asher.auel(AT)reed.edu)

Sequence in context: A083268 A085911 A058312 this_sequence A109935 A065887 A072181

Adjacent sequences: A003415 A003416 A003417 this_sequence A003419 A003420 A003421

nonn,easy,core,nice

Roland Anderson (roland.anderson(AT)swipnet.se)