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A256502
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Largest integer not exceeding the harmonic mean of the first n squares.
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3
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1, 1, 2, 2, 3, 4, 4, 5, 5, 6, 7, 7, 8, 8, 9, 10, 10, 11, 11, 12, 13, 13, 14, 14, 15, 16, 16, 17, 18, 18, 19, 19, 20, 21, 21, 22, 22, 23, 24, 24, 25, 25, 26, 27, 27, 28, 28, 29, 30, 30, 31, 31, 32, 33, 33, 34, 35, 35, 36, 36, 37, 38, 38, 39, 39, 40, 41, 41
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OFFSET
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1,3
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COMMENTS
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Least k such that 1/k <= mean of {1, 1/2^2, 1/3^2,..., 1/n^2}.
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LINKS
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FORMULA
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a(n) = floor(n/{sum{1/k^2, k = 1..n}).
Approaches asymptotically n/zeta(2), zeta being the Riemann function.
For any e > 0 and large enough n, n/zeta(2) + 36/Pi^4 - 1 < a(n) < n/zeta(2) + 36/Pi^4 + e. (Possibly this holds even with e = 0 for n > 29.) - Charles R Greathouse IV, Apr 08 2015
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MATHEMATICA
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Table[Floor[HarmonicMean[Range[n]^2]], {n, 70}] (* Harvey P. Dale, Mar 08 2020 *)
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PROG
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(PARI) \\ Using only precision-independent integer operations:
a(n)=(n*n!^2)\sum(k=1, n, (n!\k)^2)
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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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