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A226762
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Least k such that 1/k <= mean of {1, 1/2, 1/3,..., 1/n}.
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4
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1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 15, 15
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OFFSET
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1,5
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COMMENTS
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Largest integer not exceeding the harmonic mean of the first n numbers.
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LINKS
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FORMULA
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a(n) = floor(n/{sum{1/k, k = 1..n}).
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EXAMPLE
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1/3 < mean{1,1/2,1/3,...,1/9} < 1/4, so that a(9) = 3.
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MATHEMATICA
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f[n_] := Mean[Table[1/k, {k, 1, n}]]
Table[Floor[1/f[n]], {n, 1, 120}] (* A226762 *)
Table[Ceiling[1/f[n]], {n, 1, 120}] (* A226763 *)
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PROG
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(PARI) \\ This uses only precision-independent integer operations:
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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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STATUS
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approved
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