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 A346193 #12 Oct 16 2023 01:48:29
%S A346193 0,0,0,0,0,1,3,4,7,6,15,17,27,34,36,52,64,75,91,102,122,155,169,193,
%T A346193 228,263,276,326,349,415,430,500,520,620,681,727,741,881,880,1090,
%U A346193 1020,1192,1178,1375,1513,1590,1557,1809,1756,2274,2024,2323,2245,2626,2865
%N A346193 Convolution of level 5 of the divisor function.
%H A346193 Amiram Eldar, <a href="/A346193/b346193.txt">Table of n, a(n) for n = 1..10000</a>
%H A346193 Şaban Alaca and Kenneth S. Williams, <a href="https://doi.org/10.1016/j.jnt.2006.10.004">Evaluation of the convolution sums ...</a>, Journal of Number Theory, Vol. 124, No. 2 (2007) pp. 491-510.
%H A346193 Mathieu Lemire and Kenneth S. Williams, <a href="https://doi.org/10.1017/S0004972700038661">Evaluation of two convolution sums involving the sum of divisors function</a>, Bulletin of the Australian Mathematical Society, Vol. 73, No. 1 (2006), pp. 107-115.
%H A346193 Emmanuel Royer, <a href="https://doi.org/10.1142/S1793042107000924">Evaluating convolution sums of the divisor function by quasimodular forms</a>, International Journal of Number Theory, Vol. 3, No. 2 (2007) pp. 231-261.
%F A346193 a(n) = Sum_{k < n/5} sigma(k) * sigma(n-5*k).
%F A346193 a(n) = 5*sigma_3(n)/312 + 125*sigma_3(n/5)/312 + (1/24 - n/20)*sigma(n) + (1/24 - n/4)*sigma(n/5) - c_5(n)/130, where sigma_3(n/5) = sigma(n/5) = 0 if n is not divisible by 5, and c_5(n) is the coefficient of q^n in the expansion of (eta(q) * eta(q^5))^4 (A030210).
%t A346193 a[n_] := Sum[DivisorSigma[1, k] * DivisorSigma[1, n - 5*k], {k, 1, (n - 1)/5}]; Array[a, 100]
%t A346193 (* or *)
%t A346193 c[n_] := SeriesCoefficient[q * (QPochhammer[q] * QPochhammer[q^5])^4, {q, 0, n}]; a[n_] := 5 * DivisorSigma[3, n]/312 + If[Divisible[n, 5], 125 * DivisorSigma[3, n/5]/312, 0] - n * DivisorSigma[1, n]/20 - If[Divisible[n, 5], n * DivisorSigma[1, n/5]/4, 0] + DivisorSigma[1, n]/24 + If[Divisible[n, 5], DivisorSigma[1, n/5]/24, 0] - c[n]/130; Array[a, 100]
%Y A346193 Cf. A000203, A000385, A001158, A030210, A218276, A218277, A218278.
%K A346193 nonn
%O A346193 1,7
%A A346193 _Amiram Eldar_, Jul 09 2021