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A226762 Least k such that 1/k <= mean of {1, 1/2, 1/3,..., 1/n}. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,5
COMMENTS
Largest integer not exceeding the harmonic mean of the first n numbers.
LINKS
FORMULA
a(n) = floor(n/{sum{1/k, k = 1..n}).
EXAMPLE
1/3 < mean{1,1/2,1/3,...,1/9} < 1/4, so that a(9) = 3.
MATHEMATICA
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 *)
PROG
(PARI) \\ This uses only precision-independent integer operations:
a(n)=(n*n!)\sum(k=1, n, n!\k) \\ - Stanislav Sykora, Apr 08 2015
CROSSREFS
Sequence in context: A091373 A197637 A235492 * A347697 A300763 A359276
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 19 2013
STATUS
approved

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)