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A302433 a(n) is the sum of the nonmiddle divisors of n.

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%I A302433 #16 May 08 2018 07:26:44
%S A302433 0,2,4,5,6,7,8,13,10,18,12,21,14,24,16,27,18,36,20,33,32,36,24,50,26,
%T A302433 42,40,45,30,61,32,59,48,54,36,85,38,60,56,77,42,83,44,84,64,72,48,
%U A302433 110,50,88,72,98,54,105,72,105,80,90,60,152,62,96,88,119,84,127,68,126,96,127,72,172,74,114,124
%N A302433 a(n) is the sum of the nonmiddle divisors of n.
%C A302433 The nonmiddle divisors of n are here the divisors of n that are not in the half-open interval [sqrt(n/2), sqrt(n*2)).
%F A302433 a(n) = A000203(n) - A071090(n).
%e A302433 For n = 12 the divisors of 12 are [1, 2, 3, 4, 6, 12] and the middle divisors of 12 are [3, 4]. The divisors of 12 that are not middle divisors are called here the "nonmiddle" divisors of 12; they are [1, 2, 6, 12] and the sum of them is 1 + 2 + 6 + 12 = 21, so a(12) = 21.
%t A302433 Table[DivisorSum[n, # &, Or[#^2 < n/2, #^2 >= 2 n] &], {n, 75}] (* _Michael De Vlieger_, Apr 21 2018 *)
%o A302433 (PARI) a(n) = sumdiv( n, d, d*(d*d<n/2 || d*d >= 2*n)); \\ _Michel Marcus_, Apr 20 2018
%Y A302433 Cf. A000203, A067742, A067743, A071090.
%K A302433 nonn
%O A302433 1,2
%A A302433 _Omar E. Pol_, Apr 07 2018