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 A082022 In the following square array a(i,j) = Least Common Multiple of i and j. Sequence contains the product of the terms of the n-th antidiagonal. 1
 1, 4, 18, 576, 1200, 518400, 1587600, 180633600, 1646023680, 13168189440000, 461039040000, 229442532802560000, 86553098311680000, 3753113311877529600, 834966920275488000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS If n is even and n+1 is prime, a(n) = n^2 * (n-1)!^2. If n is odd and >3, 2*(n+1)*a(n) is a perfect square, the root of which has the factor 1/2*n*(n-1)*((n-1)/2)!. This was proved by Lawrence Sze. - Ralf Stephan, Nov 16 2004 LINKS Table of n, a(n) for n=1..15. FORMULA Prod(k=1...n, lcm(k, n+1-k)). EXAMPLE 1 2 3 4 5... 2 2 6 4 10... 3 6 3 12 15... 4 4 12 4 20... 5 10 15 20 5... ... The same array in triangular form is 1 2 2 3 2 3 4 6 6 4 5 4 3 4 5 ... Sequence contains the product of the terms of the n-th row. PROG (PARI) for(n=1, 20, p=1:for(k=1, n, p=p*lcm(k, n+1-k)):print1(p", ")) CROSSREFS Cf. A006580, A003990, A082292. Equals A001044(n) / A051190(n+1). Sequence in context: A214240 A156522 A086400 * A354303 A114574 A295223 Adjacent sequences: A082019 A082020 A082021 * A082023 A082024 A082025 KEYWORD nonn AUTHOR Amarnath Murthy, Apr 06 2003 EXTENSIONS Corrected and extended by Ralf Stephan, Apr 08 2003 STATUS approved

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Last modified September 7 19:14 EDT 2024. Contains 375749 sequences. (Running on oeis4.)