A073841 LCM of the composite numbers between n and 2n (both inclusive).

1, 4, 12, 24, 360, 360, 2520, 5040, 5040, 5040, 55440, 55440, 3603600, 10810800, 10810800, 21621600, 367567200, 367567200, 6983776800, 6983776800, 6983776800, 6983776800, 160626866400, 160626866400, 1124388064800, 1124388064800, 1124388064800, 1124388064800

Offset: 1

Author

Amarnath Murthy, Aug 13 2002

Keywords

• nonn
• easy

Comments

Also, smallest number divisible by all integers 1 through n as well as all composite numbers 1 through 2n. - J. Lowell, Jul 16 2008 [Definition of A140813, that is a duplicate of this sequence]

Not a subsequence of A002182: a(79) = 10703173554082014360835514860858032000 is the smallest term that is not in A002182. [Klaus Brockhaus, Aug 28 2008]

Examples

			a(6) = lcm(6,8,9,10,12) = 360.
The primes <= 10 are 2, 3, 5 and 7. Their highest powers below 2 * 10 = 20 are 16, 9, 5 and 7 respectively. Therefore, a(10) = 16 * 9 * 5 * 7 = 5040. - _David A. Corneth_, Mar 19 2018
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..2286

Crossrefs

Cf. A073839, A073640.

Programs

Maple

for n from 1 to 100 do l := 1:for j from n to 2*n do if not isprime(j) then l := lcm(l,j):fi:od:a[n] := l:od: seq(a[j],j=1..100);

Mathematica

Table[ Apply[ LCM, Select[Range[n, 2n], !PrimeQ[ # ] & ]], {n, 2, 26}]

PARI

iscomposite(x) = (x!=1) && !isprime(x);
a(n) = lcm(select(x->iscomposite(x), vector(n+1, k, n+k-1))); \\ Michel Marcus, Mar 18 2018

PARI

a(n) = my(res = 1); forprime(p = 2, n, res *= p^(logint(n<<1, p))); res \\ David A. Corneth, Mar 19 2018

Extensions

Edited by Robert G. Wilson v, Sascha Kurz and Labos Elemer, Aug 14 2002

a(1) changed to 1 by Alois P. Heinz, Mar 18 2018