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A128501
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a(n) = lcm{1 <= k <= n, gcd(k, 3) = 1}.
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4
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1, 1, 2, 2, 4, 20, 20, 140, 280, 280, 280, 3080, 3080, 40040, 40040, 40040, 80080, 1361360, 1361360, 25865840, 25865840, 25865840, 25865840, 594914320, 594914320, 2974571600, 2974571600, 2974571600, 2974571600, 86262576400
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OFFSET
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0,3
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COMMENTS
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Old name was: Denominators of partial sums for a series for Pi/(3*sqrt(3)).
The numerators are given in A128500. See the W. Lang link under A128500.
There appears to be a relationship between a(n) and b(n) = Denominator(3*HarmonicNumber(n)). For n=0..8, b(n)=a(n). For n=9..17, b(n)= 3*a(n). Starting at term 18, b(n)/a(n) = 1, 1, 1/5, 1/5, 1/5, 1/5, 1/5, 1, 1, 9, 9, 9, 9, 9, 9. - Gary Detlefs, Oct 12 2011 [adjusted to new definition by Peter Luschny, Oct 15 2012]
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LINKS
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FORMULA
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a(n+1) = denominator(r(n)) with the rationals r(n):=Sum_{k=0..n} ((-1)^k)*S(k,1)/(k+1) with Chebyshev's S-Polynomials S(n,1)=[1,1,0,-1,-1,0] periodic sequence with period 6. See A010892.
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MAPLE
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A128501 := n -> ilcm(op(select(j->igcd(j, 3) = 1, [$1..n]))):
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MATHEMATICA
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a[n_] := If[n == 0, 1, LCM @@ Select[Range[n], GCD[#, 3] == 1&]];
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PROG
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(Sage)
def A128501(n): return lcm([j for j in (1..n) if gcd(j, 3) == 1])
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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