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A130724
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a(n) = lcm(n,3) / gcd(n,3).
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5
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0, 3, 6, 1, 12, 15, 2, 21, 24, 3, 30, 33, 4, 39, 42, 5, 48, 51, 6, 57, 60, 7, 66, 69, 8, 75, 78, 9, 84, 87, 10, 93, 96, 11, 102, 105, 12, 111, 114, 13, 120, 123, 14, 129, 132, 15, 138, 141, 16, 147, 150, 17, 156, 159, 18, 165, 168, 19, 174, 177, 20, 183, 186
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: x*(3 + 6*x + x^2 + 6*x^3 + 3*x^4)/(x^3 - 1)^2.
a(n) = 2*a(n-3) - a(n-6) for n>5.
a(n) = 27*n/(5 + 4*cos(2*n*Pi/3))^2.
If n mod 3 = 0, then n/3, else 3*n.
a(n) = lcm(numerator(n/3), denominator(n/3)). (End)
Sum_{k=1..n} a(k) ~ (19/18)*n^2. - Amiram Eldar, Oct 07 2023
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EXAMPLE
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a(7) = 21 because lcm(3,7) = 21, gcd(3,7) = 1 and 21/1 = 21.
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MAPLE
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MATHEMATICA
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PROG
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CROSSREFS
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KEYWORD
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easy,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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