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 A352037 #19 Oct 11 2023 03:54:47
%S A352037 0,1,1,1,1,19684,1,1,19684,1953126,1,19684,1,40353608,1972809,1,1,
%T A352037 387440173,1,1953126,40373291,2357947692,1,19684,1953126,10604499374,
%U A352037 387440173,40353608,1,38445332184,1,1,2357967375,118587876498,42306733,387440173,1,322687697780
%N A352037 Sum of the 9th powers of the odd proper divisors of n.
%H A352037 Seiichi Manyama, <a href="/A352037/b352037.txt">Table of n, a(n) for n = 1..10000</a>
%H A352037 <a href="/index/Su#sums_of_divisors">Index entries for sequences related to sums of divisors</a>.
%F A352037 a(n) = Sum_{d|n, d<n, d odd} d^9.
%F A352037 G.f.: Sum_{k>=1} (2*k-1)^9 * x^(4*k-2) / (1 - x^(2*k-1)). - _Ilya Gutkovskiy_, Mar 02 2022
%F A352037 From _Amiram Eldar_, Oct 11 2023: (Start)
%F A352037 a(n) = A321813(n) - n^9*A000035(n).
%F A352037 Sum_{k=1..n} a(k) ~ c * n^10, where c = (zeta(10)-1)/20 = 0.0000497287... . (End)
%e A352037 a(10) = 1953126; a(10) = Sum_{d|10, d<10, d odd} d^9 = 1^9 + 5^9 = 1953126.
%t A352037 f[2, e_] := 1; f[p_, e_] := (p^(9*e+9) - 1)/(p^9 - 1); a[1] = 0; a[n_] := Times @@ f @@@ FactorInteger[n] - If[OddQ[n], n^9, 0]; Array[a, 60] (* _Amiram Eldar_, Oct 11 2023 *)
%Y A352037 Sum of the k-th powers of the odd proper divisors of n for k=0..10: A091954 (k=0), A091570 (k=1), A351647 (k=2), A352031 (k=3), A352032 (k=4), A352033 (k=5), A352034 (k=6), A352035 (k=7), A352036 (k=8), this sequence (k=9), A352038 (k=10).
%Y A352037 Cf. A000035, A013668, A321813.
%K A352037 nonn,easy
%O A352037 1,6
%A A352037 _Wesley Ivan Hurt_, Mar 01 2022