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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 (list; graph; refs; listen; history; text; internal format)
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 A103471 A114979

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

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Last modified April 19 22:40 EDT 2021. Contains 343117 sequences. (Running on oeis4.)