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A169900
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Earliest sequence such that xy | a(x+y) for all x>=1, y>=1.
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1
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1, 1, 2, 12, 12, 360, 60, 1680, 2520, 25200, 2520, 332640, 27720, 5045040, 5405400, 2882880, 720720, 220540320, 12252240, 4655851200, 4888643760, 5121436320, 232792560, 128501493120, 26771144400, 696049754400
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OFFSET
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1,3
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COMMENTS
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If n = p^d for prime p, then a(n) = p^(2*d-2)*Product_q q^floor(log_q(n)), where the product is over all primes q < n other than p.
Otherwise, a(n) = n^2*Product_p p^floor(log_p(n/p^(nu(n,p)))),
where the product is over all primes p < n and nu(n,p) is the p-adic order of n. (End)
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LINKS
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EXAMPLE
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After a(1)=a(2)=1, we must have a(3) >= 2 from 2 | a(1+2), and a(3)=2 works.
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MAPLE
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seq(ilcm(seq(x*(n-x), x=1..n/2)), n=1..50); # Robert Israel, Dec 28 2017
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MATHEMATICA
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a[n_]:=If[n<=2, 1, LCM@@Table[x(n-x), {x, Floor[n/2]}]]; Table[a[n], {n, 30}] (* Zak Seidov, Jul 11 2010 *)
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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STATUS
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approved
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