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A361879
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Sum 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, 2, 0, 2, 0, 2, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 10, 0, 0, 0, 4, 0, 6, 0, 4, 0, 0, 0, 6, 0, 0, 0, 8, 0, 6, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 6, 0, 8, 0, 0, 0, 16, 0, 0, 0, 8, 0, 6, 0, 0, 0, 10, 0, 14, 0, 0, 0, 0, 0, 0, 0, 18, 0, 0, 0, 12, 0, 0, 0, 8, 0, 10, 0, 0, 0, 0, 0, 20
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OFFSET
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1,4
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COMMENTS
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Sum of even divisors of n in the half-open interval [sqrt(n/2), sqrt(n*2)).
Also sum 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) = 4.
For n = 24 the middle divisors of 24 are [4, 6]. There are two even middle divisors of 24 so a(24) = 4 + 6 = 10.
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MAPLE
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f:= proc(n) local D;
if n::odd then return 0 fi;
D:= select(proc(d) local s; if d::odd then return false fi; s:= d^2; s >= n/2 and s < 2*n end proc, numtheory:-divisors(n)); convert(D, `+`) end proc:
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MATHEMATICA
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Table[DivisorSum[n, # &, And[EvenQ[#], Sqrt[n/2] <= # < Sqrt[2 n]] &], {n, 120}] (* Michael De Vlieger, Mar 28 2023 *)
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PROG
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(PARI) a(n) = vecsum(select(x->((x >= sqrt(n/2)) && (x < sqrt(n*2)) && !(x%2)), divisors(n))); \\ Michel Marcus, Mar 31 2023
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CROSSREFS
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Cf. A000203, A067742, A071090, A071562, A146076, A299761, A299777, A303297, A358434, A361561, A361824.
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KEYWORD
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AUTHOR
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STATUS
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approved
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