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 A239933 #24 Dec 07 2016 11:08:05 %S A239933 2,2,4,4,6,6,8,8,8,10,10,12,12,14,6,6,14,16,16,18,12,18,20,8,8,20,22, %T A239933 22,24,24,26,10,10,26,28,8,8,28,30,30,32,12,16,12,32,34,34,36,36,38, %U A239933 24,24,38,40,40,42,42,44,16,16,44,46,20,46,48,12,12,48,50,18,20,18,50,52,52,54,54,56,20,20,56,58,14,14,58,60,12,12,60,62,22,22,62,64,64 %N A239933 Triangle read by rows in which row n lists the parts of the symmetric representation of sigma(4n-1). %C A239933 Row n is a palindromic composition of sigma(4n-1). %C A239933 Row n is also the row 4n-1 of A237270. %C A239933 Row n has length A237271(4n-1). %C A239933 Row sums give A239053. %C A239933 Also row n lists the parts of the symmetric representation of sigma in the n-th arm of the third quadrant of the spiral described in A239660, see example. %C A239933 For the parts of the symmetric representation of sigma(4n-3), see A239931. %C A239933 For the parts of the symmetric representation of sigma(4n-2), see A239932. %C A239933 For the parts of the symmetric representation of sigma(4n), see A239934. %C A239933 We can find the spiral (mentioned above) on the terraces of the pyramid described in A244050. - _Omar E. Pol_, Dec 06 2016 %e A239933 The irregular triangle begins: %e A239933 2, 2; %e A239933 4, 4; %e A239933 6, 6; %e A239933 8, 8, 8; %e A239933 10, 10; %e A239933 12, 12; %e A239933 14, 6, 6, 14; %e A239933 16, 16; %e A239933 18, 12, 18; %e A239933 20, 8, 8, 20; %e A239933 22, 22; %e A239933 24, 24; %e A239933 26, 10, 10, 26; %e A239933 28, 8, 8, 28; %e A239933 30, 30; %e A239933 32, 12, 16, 12, 32; %e A239933 ... %e A239933 Illustration of initial terms in the third quadrant of the spiral described in A239660: %e A239933 . _ _ _ _ _ _ _ _ %e A239933 . | | | | | | | | | | | | | | | | %e A239933 . | | | | | | | | | | | | | | |_|_ _ %e A239933 . | | | | | | | | | | | | | | 2 |_ _| %e A239933 . | | | | | | | | | | | | |_|_ 2 %e A239933 . | | | | | | | | | | | | 4 |_ %e A239933 . | | | | | | | | | | |_|_ _ |_ _ _ _ %e A239933 . | | | | | | | | | | 6 |_ |_ _ _ _| %e A239933 . | | | | | | | | |_|_ _ _ |_ 4 %e A239933 . | | | | | | | | 8 | |_ _ | %e A239933 . | | | | | | |_|_ _ _ |_ | |_ _ _ _ _ _ %e A239933 . | | | | | | 10 | |_ |_ |_ _ _ _ _ _| %e A239933 . | | | | |_|_ _ _ _ |_ _ 8 |_ _| 6 %e A239933 . | | | | 12 | |_ | %e A239933 . | | |_|_ _ _ _ _ |_ _ | |_ _ _ _ _ _ _ _ %e A239933 . | | 14 | | |_ |_ _ |_ _ _ _ _ _ _ _| %e A239933 . |_|_ _ _ _ _ | |_ _ |_ | 8 %e A239933 . 16 | |_ _ | | | %e A239933 . | |_|_ |_ _ |_ _ _ _ _ _ _ _ _ _ %e A239933 . |_ _ 6 |_ _ | |_ _ _ _ _ _ _ _ _ _| %e A239933 . | |_ | | 10 %e A239933 . |_ 6 | |_ _ | %e A239933 . |_ |_ _ _| |_ _ _ _ _ _ _ _ _ _ _ _ %e A239933 . |_ _ | |_ _ _ _ _ _ _ _ _ _ _ _| %e A239933 . | | 12 %e A239933 . |_ _ _ | %e A239933 . | |_ _ _ _ _ _ _ _ _ _ _ _ _ _ %e A239933 . | |_ _ _ _ _ _ _ _ _ _ _ _ _ _| %e A239933 . | 14 %e A239933 . | %e A239933 . |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ %e A239933 . |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| %e A239933 . 16 %e A239933 . %e A239933 For n = 7 we have that 4*7-1 = 27 and the 27th row of A237593 is [14, 5, 3, 2, 1, 2, 2, 1, 2, 3, 5, 14] and the 26th row of A237593 is [14, 5, 2, 2, 2, 1, 1, 2, 2, 2, 5, 14] therefore between both Dyck paths there are four regions (or parts) of sizes [14, 6, 6, 14], so row 7 is [14, 6, 6, 14]. %e A239933 The sum of divisors of 27 is 1 + 3 + 9 + 27 = A000203(27) = 40. On the other hand the sum of the parts of the symmetric representation of sigma(27) is 14 + 6 + 6 + 14 = 40, equaling the sum of divisors of 27. %Y A239933 Cf. A000203, A196020, A236104, A235791, A237270, A237271, A237591, A237593, A239053, A239660, A239931, A239932, A239934, A244050, A245092, A262626. %K A239933 nonn,tabf %O A239933 1,1 %A A239933 _Omar E. Pol_, Mar 29 2014