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A212607
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Number of distinct sums <= 1 of distinct reciprocals of integers <= n.
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3
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1, 2, 3, 5, 8, 14, 21, 38, 70, 129, 238, 440, 504, 949, 1790, 2301, 4363, 8272, 12408, 23604, 26675, 45724, 87781, 168549, 181989, 351076, 677339, 1306894, 1399054, 2709128, 2795144, 5423805, 10525050
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OFFSET
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0,2
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LINKS
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EXAMPLE
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a(3) = 5 counts numbers { 0, 1/3, 1/2, 5/6, 1 }, each of which is can be represented as the sum of distinct reciprocals 1/1, 1/2, and 1/3.
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MAPLE
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s:= proc(n) option remember;
`if`(n=0, {0}, map(x-> `if`(n-1<n*x, x, [x, x+1/n][]), s(n-1)))
end:
a:= n-> nops(s(n)):
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MATHEMATICA
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s[_] := s[n] = If[n == 0, {0}, If[n-1 < n*#, #, {#, # + 1/n}]& /@ s[n-1] // Flatten];
a[n_] := Length[s[n]];
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CROSSREFS
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For possibly non-distinct reciprocals, see A212606.
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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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