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%I #38 Mar 22 2018 05:12:19
%S 1,4,12,24,360,360,2520,5040,5040,5040,55440,55440,3603600,10810800,
%T 10810800,21621600,367567200,367567200,6983776800,6983776800,
%U 6983776800,6983776800,160626866400,160626866400,1124388064800,1124388064800,1124388064800,1124388064800
%N LCM of the composite numbers between n and 2n (both inclusive).
%C 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]
%C Not a subsequence of A002182: a(79) = 10703173554082014360835514860858032000 is the smallest term that is not in A002182. [_Klaus Brockhaus_, Aug 28 2008]
%H David A. Corneth, <a href="/A073841/b073841.txt">Table of n, a(n) for n = 1..2286</a>
%e a(6) = lcm(6,8,9,10,12) = 360.
%e 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
%p 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);
%t Table[ Apply[ LCM, Select[Range[n, 2n], !PrimeQ[ # ] & ]], {n, 2, 26}]
%o (PARI) iscomposite(x) = (x!=1) && !isprime(x);
%o a(n) = lcm(select(x->iscomposite(x), vector(n+1, k, n+k-1))); \\ _Michel Marcus_, Mar 18 2018
%o (PARI) a(n) = my(res = 1); forprime(p = 2, n, res *= p^(logint(n<<1, p))); res \\ _David A. Corneth_, Mar 19 2018
%Y Cf. A073839, A073640.
%K nonn,easy
%O 1,2
%A _Amarnath Murthy_, Aug 13 2002
%E Edited by _Robert G. Wilson v_, _Sascha Kurz_ and _Labos Elemer_, Aug 14 2002
%E a(1) changed to 1 by _Alois P. Heinz_, Mar 18 2018
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