

A073841


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


2



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
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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+k1))); \\ 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



