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

1,2

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]

Links

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

Example

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

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}]

Prog

(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

Crossrefs

Cf. A073839, A073640.

Sequence in context: A199903 A218034 A140813 * A032339 A345893 A103471

Adjacent sequences: A073838 A073839 A073840 * A073842 A073843 A073844

Keyword

nonn,easy

Author

Amarnath Murthy, Aug 13 2002

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

Status

approved