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A306904
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The geometric mean of the first n integers, rounded to the nearest integer.
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1
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1, 1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 14, 14, 14, 15, 15, 15, 16, 16, 17, 17, 17, 18, 18, 18, 19, 19, 19, 20, 20, 21, 21, 21, 22, 22, 22, 23, 23, 24, 24, 24, 25, 25, 25
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OFFSET
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1,3
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COMMENTS
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a(n) is the least k such that (k-1/2)^n < n!. - Robert Israel, May 05 2019
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LINKS
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FORMULA
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a(n) = round(n!^(1/n)).
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EXAMPLE
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a(5) is the 5th root of the product of the first 5 integers (approx. 2.605171) rounded up to 3.
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MAPLE
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Res:= 1: last:= 1: v:= 1:
for n from 2 to 100 do
v:= n*v; t:= 2^n*v;
for k from last while (2*k-1)^n < t do od:
last:= k-1;
Res:= Res, last;
od:
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MATHEMATICA
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Table[Round[GeometricMean[Range[n]]], {n, 70}] (* Harvey P. Dale, Mar 19 2023 *)
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PROG
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CROSSREFS
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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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