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A346869 Sum of all divisors, except the smallest and the largest of every number, of the first n odd numbers.

%I A346869 #33 Jul 29 2023 14:24:04
%S A346869 0,0,0,0,3,3,3,11,11,11,21,21,26,38,38,38,52,64,64,80,80,80,112,112,
%T A346869 119,139,139,155,177,177,177,217,235,235,261,261,261,309,327,327,366,
%U A346869 366,388,420,420,440,474,498,498,554,554,554,640,640,640,680,680,708,772,796
%N A346869 Sum of all divisors, except the smallest and the largest of every number, of the first n odd numbers.
%C A346869 Partial sums of the odd-indexed terms of Chowla's function A048050.
%C A346869 a(n) has a symmetric representation.
%p A346869 a:= proc(n) option remember; `if`(n=1, 0,
%p A346869       a(n-1)+numtheory[sigma](2*n-1)-2*n)
%p A346869     end:
%p A346869 seq(a(n), n=1..60);  # _Alois P. Heinz_, Aug 19 2021
%t A346869 s[1] = 0; s[n_] := DivisorSigma[1, 2*n - 1] - 2*n; Accumulate @ Array[s, 50] (* _Amiram Eldar_, Aug 19 2021 *)
%t A346869 Accumulate[Join[{0},Table[DivisorSigma[1,n]-n-1,{n,3,151,2}]]] (* _Harvey P. Dale_, Jul 29 2023 *)
%o A346869 (Python)
%o A346869 from sympy import divisors
%o A346869 from itertools import accumulate
%o A346869 def A346879(n): return sum(divisors(2*n-1)[1:-1])
%o A346869 def aupton(nn): return list(accumulate(A346879(n) for n in range(1, nn+1)))
%o A346869 print(aupton(60)) # _Michael S. Branicky_, Aug 19 2021
%Y A346869 Partial sums of A346879.
%Y A346869 Cf. A000203, A005408, A008438, A048050, A237593, A245092, A244049, A326123, A346870.
%K A346869 nonn,easy
%O A346869 1,5
%A A346869 _Omar E. Pol_, Aug 18 2021