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 A060047 #23 Sep 16 2023 10:41:08
%S A060047 1,2,4,1,4,2,6,4,8,8,8,14,8,1,18,13,2,28,12,4,40,12,8,52,16,14,70,14,
%T A060047 24,88,16,40,104,24,1,56,140,16,2,84,168,18,4,122,196,26,8,168,240,20,
%U A060047 14,232,278,24,24,312,320,32,40,408,380,24,64,528,440,24,100,672,504
%N A060047 Triangle of generalized sum of divisors function, read by rows.
%C A060047 Lengths of rows are 1 1 1 2 2 2 2 2 3 3 3 3 3 3 3 ... (A000196).
%H A060047 G. E. Andrews and S. C. F. Rose, <a href="http://arxiv.org/abs/1010.5769">MacMahon's sum-of-divisors functions, Chebyshev polynomials, and Quasi-modular forms</a>, arXiv:1010.5769 [math.NT], 2010.
%H A060047 P. A. MacMahon, <a href="https://doi.org/10.1112/plms/s2-19.1.75">Divisors of numbers and their continuations in the theory of partitions</a>, Proc. London Math. Soc., 19 (1919), 75-113; Coll. Papers II, pp. 303-341.
%F A060047 T(n, k) = sum of s_1*s_2*...*s_k where s_1, s_2, ..., s_k are such that s_1*(2*m_1-1) + s_2*(2*m_2-1) + ... + s_k*(2*m_k-1) = n and the sum is over all such k-partitions of n.
%F A060047 G.f. for k-th diagonal (the k-th row of the sideways triangle shown in the example): Sum_{ m_1 < m_2 < ... < m_k} q^(2*m_1+2*m_2+...+2*m_k-k)/((1-q^{2*m_1-1})*(1-q^{2*m_2-1})*...*(1-q^{2*m_k-1}))^2 = Sum_n T(n, k)*q^n.
%F A060047 G.f. for k-th diagonal: (-1)^k * (1/k) * ( Sum_{j>=k} (-1)^j * j * binomial(j+k-1,2*k-1) * q^(j^2) ) / ( 1 + 2 * Sum_{j>=1} (-q)^(j^2) ). - _Seiichi Manyama_, Sep 15 2023
%e A060047 Triangle turned on its side begins:
%e A060047 1 2 4 4 6 8 8 8 13 12 12 ...
%e A060047 1 2 4 8 14 18 28 40 ...
%e A060047 1 2 4 ...
%e A060047 For example, T(6,1) = 8, T(6,2) = 4.
%Y A060047 Diagonals give A002131, A002132, A060046, A365666, A365667.
%Y A060047 Cf. A060043, A060044, A060177, A060184.
%K A060047 nonn,tabf,easy,nice
%O A060047 1,2
%A A060047 _N. J. A. Sloane_, Mar 19 2001
%E A060047 More terms from _Naohiro Nomoto_, Jan 24 2002