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A361561
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Number of even middle divisors of n, where "middle divisor" means a divisor in the half-open interval [sqrt(n/2), sqrt(n*2)).
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2
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0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 1, 0
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OFFSET
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1,24
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COMMENTS
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Number of even divisors of n in the half-open interval [sqrt(n/2), sqrt(n*2)).
Also number of even numbers in the n-th row of A299761.
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LINKS
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FORMULA
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EXAMPLE
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For n = 18 the middle divisor of 18 is [3]. There are no even middle divisors of 18 so a(18) = 0.
For n = 20 the middle divisors of 20 are [4, 5]. There is only one even middle divisor of 20 so a(20) = 1.
For n = 24 the middle divisors of 24 are [4, 6]. There are two even middle divisors of 24 so a(24) = 2.
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MATHEMATICA
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a[n_] := Count[Divisors[n], _?(EvenQ[#] && Sqrt[n/2] <= # < Sqrt[2*n] &)]; Array[a, 100] (* Amiram Eldar, Mar 16 2023 *)
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PROG
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(PARI) a(n) = sumdiv(n, d, if (!(d%2), (d>=sqrt(n/2)) && (d<sqrt(2*n)))); \\ Michel Marcus, Mar 15 2023
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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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