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A361879 Sum of even middle divisors of n, where "middle divisor" means a divisor in the half-open interval [sqrt(n/2), sqrt(n*2)).

%I A361879 #23 Mar 18 2024 16:52:21
%S A361879 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,
%T A361879 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,
%U A361879 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
%N A361879 Sum of even middle divisors of n, where "middle divisor" means a divisor in the half-open interval [sqrt(n/2), sqrt(n*2)).
%C A361879 Sum of even divisors of n in the half-open interval [sqrt(n/2), sqrt(n*2)).
%C A361879 Also sum of even numbers in the n-th row of A299761.
%H A361879 Robert Israel, <a href="/A361879/b361879.txt">Table of n, a(n) for n = 1..10000</a>
%H A361879 Michael De Vlieger, <a href="/A361879/a361879.png">Log log scatterplot of a(n)</a> n = 1..2^16 (ignoring zeros).
%F A361879 a(n) = A071090(n) - A361824(n).
%e A361879 For n = 18 the middle divisor of 18 is [3]. There are no even middle divisors of 18 so a(18) = 0.
%e A361879 For n = 20 the middle divisors of 20 are [4, 5]. There is only one even middle divisor of 20 so a(20) = 4.
%e A361879 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.
%p A361879 f:= proc(n) local D;
%p A361879      if n::odd then return 0 fi;
%p A361879      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:
%p A361879 map(f, [$1..100]); # _Robert Israel_, Mar 18 2024
%t A361879 Table[DivisorSum[n, # &, And[EvenQ[#], Sqrt[n/2] <= # < Sqrt[2 n]] &], {n, 120}] (* _Michael De Vlieger_, Mar 28 2023 *)
%o A361879 (PARI) a(n) = vecsum(select(x->((x >= sqrt(n/2)) && (x < sqrt(n*2)) && !(x%2)), divisors(n))); \\ _Michel Marcus_, Mar 31 2023
%Y A361879 Cf. A000203, A067742, A071090, A071562, A146076, A299761, A299777, A303297, A358434, A361561, A361824.
%K A361879 nonn,look
%O A361879 1,4
%A A361879 _Omar E. Pol_, Mar 27 2023