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%I #20 Aug 20 2021 00:23:14
%S 0,0,0,0,3,0,0,8,0,0,10,0,5,12,0,0,14,12,0,16,0,0,32,0,7,20,0,16,22,0,
%T 0,40,18,0,26,0,0,48,18,0,39,0,22,32,0,20,34,24,0,56,0,0,86,0,0,40,0,
%U 28,64,24,11,44,30,0,46,0,26,104,0,0,50,24,34,80,0,0,80,36
%N Sum of the divisors, except the smallest and the largest, of the n-th odd number.
%C a(n) has a symmetric representation.
%F a(n) = A048050(2*n-1).
%e For n = 5 the 5th odd number is 9 and the divisors of 9 are [1, 3, 9] and the sum of the divisors of 9 except the smaller and the largest is 3, so a(5) = 3.
%e For n = 6 the 6th odd number is 11 and the divisors of 11 are [1, 11] and the sum of the divisors of 11 except the smaller and the largest is 0, so a(6) = 0.
%t a[1] = 0; a[n_] := DivisorSigma[1, 2*n - 1] - 2*n; Array[a, 100] (* _Amiram Eldar_, Aug 19 2021 *)
%o (Python)
%o from sympy import divisors
%o def a(n): return sum(divisors(2*n-1)[1:-1])
%o print([a(n) for n in range(1, 79)]) # _Michael S. Branicky_, Aug 19 2021
%Y Bisection of A048050.
%Y Partial sums give A346869.
%Y Cf. A000203, A005408, A008438, A237593, A245092, A244049, A326123, A346880.
%K nonn,easy
%O 1,5
%A _Omar E. Pol_, Aug 18 2021