This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A347153 #27 Mar 21 2024 08:36:17
%S A347153 0,1,2,3,7,8,9,18,19,20,31,32,38,51,52,53,68,81,82,99,100,101,134,135,
%T A347153 143,164,165,182,205,206,207,248,267,268,295,296,297,346,365,366,406,
%U A347153 407,430,463,464,485,520,545,546,603,604,605,692,693,694,735,736,765,830,855
%N A347153 Sum of all divisors, except the largest of every number, of the first n odd numbers.
%C A347153 Sum of all aliquot divisors (or aliquot parts) of the first n odd numbers.
%C A347153 Partial sums of the odd-indexed terms of A001065.
%C A347153 a(n) has a symmetric representation.
%F A347153 a(n) = A001477(n-1) + A346869(n).
%F A347153 G.f.: (1/(1 - x)) * Sum_{k>=0} (2*k + 1) * x^(3*k + 2) / (1 - x^(2*k + 1)). - _Ilya Gutkovskiy_, Aug 20 2021
%F A347153 a(n) = (Pi^2/8 - 1)*n^2 + O(n*log(n)). - _Amiram Eldar_, Mar 21 2024
%t A347153 s[n_] := DivisorSigma[1, 2*n - 1] - 2*n + 1; Accumulate @ Array[s, 100] (* _Amiram Eldar_, Aug 20 2021 *)
%o A347153 (Python)
%o A347153 from sympy import divisors
%o A347153 from itertools import accumulate
%o A347153 def A346877(n): return sum(divisors(2*n-1)[:-1])
%o A347153 def aupton(nn): return list(accumulate(A346877(n) for n in range(1, nn+1)))
%o A347153 print(aupton(60)) # _Michael S. Branicky_, Aug 20 2021
%o A347153 (PARI) a(n) = sum(k=1, n, k = 2*k-1; sigma(k)-k); \\ _Michel Marcus_, Aug 20 2021
%Y A347153 Partial sums of A346877.
%Y A347153 Cf. A000203, A001065, A001477, A005408, A008438, A048050, A153485, A237593, A245092, A244049, A326123, A346869, A346878, A346879, A347154.
%K A347153 nonn,easy
%O A347153 1,3
%A A347153 _Omar E. Pol_, Aug 20 2021