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A226037
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a(n) = Sum_{c in P(n)} lcm(c) where P(n) is the set of all subsets of {1,2,...,n}.
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2
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1, 2, 6, 24, 88, 528, 1392, 11136, 41856, 192192, 516032, 6192384, 13270272, 185783808, 511526400, 1163742720, 4403449344, 79262088192, 199280729088, 3985614581760, 8463108648960, 19276630732800, 54618972549120, 1310855341178880, 2751134770298880, 17228042511482880
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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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a(n) = Sum_{k=0..n} Sum_{c in binomial(n,k)} lcm(c) where C(n,k) are the combinations of n with size k.
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EXAMPLE
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a(4) = lcm{} + lcm{1} + lcm{2} + lcm{3} + lcm{4} + lcm{1,2} + lcm{1,3} + lcm{1,4} + lcm{2,3} + lcm{2,4} + lcm{3,4} + lcm{1,2,3} + lcm{1,2,4} + lcm{1,3,4} + lcm{2,3,4} + lcm{1,2,3,4} =
1 + 1 + 2 + 3 + 4 + 2 + 3 + 4 + 6 + 4 + 12 + 6 + 4 + 12 + 12 + 12 = 88.
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MAPLE
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with(combstruct):
A226037 := proc(n) local R, c; R := 0; c := iterstructs(Combination(n)):
while not finished(c) do R := R + ilcm(op(nextstruct(c))) od; R end: seq(A226037(n), n=0..25);
# second Maple program:
b:= proc(n, m) option remember; `if`(n=0, m,
b(n-1, ilcm(m, n))+b(n-1, m))
end:
a:= n-> b(n, 1):
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MATHEMATICA
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a[n_] := Total[LCM @@@ Rest[Subsets[Range[n]]]] + 1; Table[Print[an = a[n]]; an, {n, 0, 25}] (* Jean-François Alcover, Jan 15 2014 *)
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PROG
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@CachedFunction
def C(n, k):
if k == 0: return [1]
w = C(n-1, k) if k < n else [0]
return w + [lcm(c, n) for c in C(n-1, k-1)]
def A226037(n): return add(add(C(n, k)) for k in (0..n))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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