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Search: id:A082022
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| A082022 |
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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. |
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+0
2
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| 1, 4, 18, 576, 1200, 518400, 1587600, 180633600, 1646023680, 13168189440000, 461039040000, 229442532802560000, 86553098311680000, 3753113311877529600, 834966920275488000000
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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
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FORMULA
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Prod(k=1...n, lcm(k, n+1-k)).
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EXAMPLE
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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.
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PROGRAM
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(PARI) for(n=1, 20, p=1:for(k=1, n, p=p*lcm(k, n+1-k)):print1(p", "))
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CROSSREFS
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Cf. A006580, A003990, A082292.
Equals A001044(n) / A051190(n+1).
Sequence in context: A145660 A156522 A086400 this_sequence A114574 A156491 A069874
Adjacent sequences: A082019 A082020 A082021 this_sequence A082023 A082024 A082025
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Apr 06 2003
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EXTENSIONS
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Corrected and extended by Ralf Stephan (ralf(AT)ark.in-berlin.de), Apr 08 2003
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