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A051538
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Least common multiple of {b(1),...,b(n)}, where b(k) = k(k+1)(2k+1)/6 = A000330(k).
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5
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1, 5, 70, 210, 2310, 30030, 60060, 1021020, 19399380, 19399380, 446185740, 2230928700, 6692786100, 194090796900, 12033629407800, 12033629407800, 12033629407800, 445244288088600, 445244288088600, 18255015811632600
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OFFSET
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1,2
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COMMENTS
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Also a(n) = lcm(1,...,(2n+2))/12. - Paul Barry, Jun 09 2006. Proof that this is the same sequence, from Martin Fuller, May 06 2007: k, k+1, 2k+1 are coprime so their lcm is the same as their product. Hence a(n) = lcm{k, k+1, 2k+1 | k=1..n}/6. {k, k+1, 2k+1 | k=1..n} = {1..2n+2 excluding even numbers >n+1}. Adding the higher even numbers to the set doubles the LCM. Hence lcm{k, k+1, 2k+1 | k=1..n}/6 = lcm{1..2n+2}/12.
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LINKS
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EXAMPLE
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a(4) = lcm(1, 5, 14, 30) = 210.
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MATHEMATICA
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PROG
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(Haskell)
a051538 n = a051538_list !! (n-1)
a051538_list = scanl1 lcm $ tail a000330_list
(Magma) [Lcm([1..2*n+2])/12: n in [1..30]]; // G. C. Greubel, May 03 2023
(SageMath)
return lcm(range(1, 2*n+3))/12
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CROSSREFS
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KEYWORD
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easy,nice,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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