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 A231347 #35 Dec 22 2020 08:04:06
%S A231347 0,1,2,1,3,0,4,3,5,0,1,6,5,0,7,0,0,8,7,3,9,0,0,1,10,9,0,0,11,0,5,0,12,
%T A231347 11,0,0,13,0,0,3,14,13,7,0,1,15,0,0,0,0,16,15,0,0,0,17,0,9,5,0,18,17,
%U A231347 0,0,0,19,0,0,0,3,20,19,11,0,0,1,21,0,0,7,0,0
%N A231347 Triangle read by rows: T(n,k), n>=1, k>=1, in which column k lists the odd numbers interleaved with k-1 zeros but T(n,1) = n - 1 and the first element of column k is in row k(k+1)/2.
%C A231347 Alternating sum of row n equals the sum of aliquot divisors of n, i.e., sum_{k=1..A003056(n)} (-1)^(k-1)*T(n,k) = A001065(n).
%C A231347 Row n has length A003056(n).
%C A231347 Column k starts in row A000217(k).
%C A231347 The number of positive terms in row n is A001227(n), for n >= 2.
%C A231347 If n = 2^j then the only positive integer in row n is T(n,1) = n - 1, for j >= 1.
%C A231347 If n is an odd prime then the only two positive integers in row n are T(n,1) = n - 1 and T(n,2) = n - 2.
%F A231347 T(n,1) = n - 1.
%F A231347 T(n,k) = A196020(n,k), for k >= 2.
%e A231347 Triangle begins:
%e A231347 0;
%e A231347 1;
%e A231347 2, 1;
%e A231347 3, 0;
%e A231347 4, 3;
%e A231347 5, 0, 1;
%e A231347 6, 5, 0;
%e A231347 7, 0, 0;
%e A231347 8, 7, 3;
%e A231347 9, 0, 0, 1;
%e A231347 10, 9, 0, 0;
%e A231347 11, 0, 5, 0;
%e A231347 12, 11, 0, 0;
%e A231347 13, 0, 0, 3;
%e A231347 14, 13, 7, 0, 1;
%e A231347 15, 0, 0, 0, 0;
%e A231347 16, 15, 0, 0, 0;
%e A231347 17, 0, 9, 5, 0;
%e A231347 18, 17, 0, 0, 0;
%e A231347 19, 0, 0, 0, 3;
%e A231347 20, 19, 11, 0, 0, 1;
%e A231347 21, 0, 0, 7, 0, 0;
%e A231347 22, 21, 0, 0, 0, 0;
%e A231347 23, 0, 13, 0, 0, 0;
%e A231347 ...
%e A231347 For n = 15 the aliquot divisors of 15 are 1, 3, 5, therefore the sum of aliquot divisors of 15 is 1 + 3 + 5 = 9. On the other hand the 15th row of triangle is 14, 13, 7, 0, 1, hence the alternating row sum is 14 - 13 + 7 - 0 + 1 = 9, equalling the sum of aliquot divisors of 15.
%e A231347 If n is even then the alternating sum of the n-th row of triangle is simpler than the sum of aliquot divisors of n. Example: the sum of aliquot divisors of 24 is 1 + 2 + 3 + 4 + 6 + 8 + 12 = 36, and the alternating sum of the 24th row of triangle is 23 - 0 + 13 - 0 + 0 - 0 = 36.
%Y A231347 Columns 1-2: A001477, A193356.
%Y A231347 Cf. A000217, A001065, A001227, A000203, A003056, A196020, A211343, A212119, A228813, A231345, A235791, A235794, A236104, A236106, A236112, A237591, A237593, A286001.
%K A231347 nonn,tabf
%O A231347 1,3
%A A231347 _Omar E. Pol_, Dec 28 2013