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A096125
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Least value of k such that n!/((n-k)!)^2 is an integer.
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2
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1, 1, 2, 2, 3, 3, 4, 4, 5, 4, 5, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 13, 14, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 26, 27, 28, 29, 29, 30, 30, 31, 31, 32, 32, 33, 33, 34, 34, 35, 35, 36, 36, 37, 37, 38
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OFFSET
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1,3
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COMMENTS
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If p is the first prime > n/2, then a(n) > n-p. - Robert Israel, Jun 27 2018
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LINKS
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EXAMPLE
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a(10) = 4.
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MAPLE
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f:= proc(n) local p, k;
p:= nextprime(floor(n/2));
for k from n-p+1 do
if (n!/((n-k)!)^2)::integer then return k fi
od
end proc:
f(1):= 1:
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MATHEMATICA
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f[n_] := Block[{i = 1, t = Table[n!/(n - k)!^2, {k, n}]}, While[ !IntegerQ[ t[[i]]], i++ ]; i]; Table[ f[n], {n, 75}] (* Robert G. Wilson v, Jul 03 2004 *)
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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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