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A159553
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a(n) = Sum_{k=0..n} binomial(n,k) * gcd(n,k).
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3
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2, 6, 12, 28, 40, 144, 140, 536, 864, 2560, 2068, 12720, 8216, 45192, 78660, 182832, 131104, 933984, 524324, 3698240, 4890648, 13345816, 8388652, 67390464, 60129600, 225470544, 279938160, 1032462256, 536870968, 5018059200
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OFFSET
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1,1
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COMMENTS
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For the purpose of this sequence, gcd(n,0) = n, for all positive integers n.
a(n) is a multiple of n, for all nonnegative integers n.
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LINKS
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FORMULA
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a(n) = 2^n * Sum_{d|n} (phi(d)/d) * Sum_{k=1..d} (-1)^(k*n/d)*cos(k*Pi/d)^n.
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MAPLE
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MATHEMATICA
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Table[Sum[Binomial[n, k] GCD[n, k], {k, 0, n}], {n, 30}] (* Michael De Vlieger, Oct 30 2017 *)
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CROSSREFS
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KEYWORD
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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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