%I #38 Mar 27 2023 22:36:19
%S 1,1,0,0,0,3,0,0,3,0,0,3,0,0,8,0,0,3,0,5,0,0,0,0,5,0,0,7,0,5,0,0,0,0,
%T 12,0,0,0,0,5,0,7,0,0,14,0,0,0,7,5,0,0,0,9,0,7,0,0,0,0,0,0,16,0,0,11,
%U 0,0,0,7,0,9,0,0,0,0,18,0,0,0,9,0,0,7,0,0,0,11,0,9,20,0,0,0,0,0,0,7,20,0
%N Sum of odd middle divisors of n, where "middle divisor" means a divisor in the half-open interval [sqrt(n/2), sqrt(n*2)).
%C Sum of odd divisors of n in the half-open interval [sqrt(n/2), sqrt(n*2)) (cf. A067742).
%C Also sum of odd numbers in the n-th row of A299761.
%H Winston de Greef, <a href="/A361824/b361824.txt">Table of n, a(n) for n = 1..10000</a>
%H Michael De Vlieger, <a href="/A361824/a361824.png">Log log scatterplot of a(n)</a>, n = 1..2^16.
%H Michael De Vlieger, <a href="/A361824/a361824_1.png">Detail of scalar scatterplot of a(n)</a>, n = 1..2^16, a(n) <= 384.
%F a(n) = A071090(n) - A361879(n).
%e For n = 8 the middle divisor of 8 is [2]. There are no odd middle divisors of 8 so a(8) = 0.
%e For n = 12 the middle divisors of 12 are [3, 4]. There is only one odd middle divisor of 12 so a(12) = 3.
%e For n = 15 the middle divisors of 15 are [3, 5]. There are two odd middle divisors of 15 so a(15) = 3 + 5 = 8.
%t Table[Total@ Select[Divisors[n], And[Sqrt[n/2] <= # < Sqrt[2 n], OddQ[#] ] &], {n, 100}] (* _Michael De Vlieger_, Mar 27 2023 *)
%o (PARI) a(n) = vecsum(select(x->((x >= sqrt(n/2)) && (x < sqrt(n*2)) && x%2), divisors(n))); \\ _Michel Marcus_, Mar 26 2023
%Y Cf. A000203, A000593, A067742, A071090, A071562, A299761, A299777, A303297, A358434, A361879.
%K nonn,look
%O 1,6
%A _Omar E. Pol_, Mar 25 2023