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 A346741 #51 Aug 04 2021 03:16:06 %S A346741 1,1,1,2,1,1,2,1,3,1,1,1,2,1,3,1,1,2,4,1,2,1,1,1,2,1,3,1,1,2,4,1,2,1, %T A346741 1,5,1,3,1,2,1,1,1,1,2,1,3,1,1,2,4,1,2,1,1,5,1,3,1,2,1,1,1,2,3,6,1,2, %U A346741 4,1,3,1,2,1,2,1,1,1,7,1,5,1,2,4,1,3,1,3,1,2,1,2,1,1,1,1 %N A346741 Irregular triangle read by rows which is constructed in row n replacing the first A000070(n-1) terms of A336811 with their divisors. %C A346741 The terms in row n are also all parts of all partitions of n. %C A346741 The terms of row n in nonincreasing order give the n-th row of A302246. %C A346741 The terms of row n in nondecreasing order give the n-th row of A302247. %C A346741 For further information about the correspondence divisor/part see A336811 and A338156. %e A346741 Triangle begins: %e A346741 [1]; %e A346741 [1],[1, 2]; %e A346741 [1],[1, 2],[1, 3],[1]; %e A346741 [1],[1, 2],[1, 3],[1],[1, 2, 4],[1, 2],[1]; %e A346741 [1],[1, 2],[1, 3],[1],[1, 2, 4],[1, 2],[1],[1, 5],[1, 3],[1, 2],[1],[1]; %e A346741 ... %e A346741 Below the table shows the correspondence divisor/part. %e A346741 |---|-----------------|-----|-------|---------|-----------|-------------| %e A346741 | n | | 1 | 2 | 3 | 4 | 5 | %e A346741 |---|-----------------|-----|-------|---------|-----------|-------------| %e A346741 | P | | | | | | | %e A346741 | A | | | | | | | %e A346741 | R | | | | | | | %e A346741 | T | | | | | | 5 | %e A346741 | I | | | | | | 3 2 | %e A346741 | T | | | | | 4 | 4 1 | %e A346741 | I | | | | | 2 2 | 2 2 1 | %e A346741 | O | | | | 3 | 3 1 | 3 1 1 | %e A346741 | N | | | 2 | 2 1 | 2 1 1 | 2 1 1 1 | %e A346741 | S | | 1 | 1 1 | 1 1 1 | 1 1 1 1 | 1 1 1 1 1 | %e A346741 ----|-----------------|-----|-------|---------|-----------|-------------| %e A346741 . %e A346741 |---|-----------------|-----|-------|---------|-----------|-------------| %e A346741 | | A181187 | 1 | 3 1 | 6 2 1 | 12 5 2 1 | 20 8 4 2 1 | %e A346741 | L | | | | |/| | |/|/| | |/|/|/| | |/|/|/|/| | %e A346741 | I | A066633 | 1 | 2 1 | 4 1 1 | 7 3 1 1 | 12 4 2 1 1 | %e A346741 | N | | * | * * | * * * | * * * * | * * * * * | %e A346741 | K | A002260 | 1 | 1 2 | 1 2 3 | 1 2 3 4 | 1 2 3 4 5 | %e A346741 | | | = | = = | = = = | = = = = | = = = = = | %e A346741 | | A138785 | 1 | 2 2 | 4 2 3 | 7 6 3 4 | 12 8 6 4 5 | %e A346741 |---|-----------------|-----|-------|---------|-----------|-------------| %e A346741 . %e A346741 . |-------| %e A346741 . |Section| %e A346741 |---|-------|---------|-----|-------|---------|-----------|-------------| %e A346741 | | 1 | A000012 | 1 | 1 | 1 | 1 | 1 | %e A346741 | |-------|---------|-----|-------|---------|-----------|-------------| %e A346741 | | 2 | A000034 | | 1 2 | 1 2 | 1 2 | 1 2 | %e A346741 | |-------|---------|-----|-------|---------|-----------|-------------| %e A346741 | D | 3 | A010684 | | | 1 3 | 1 3 | 1 3 | %e A346741 | I | | A000012 | | | 1 | 1 | 1 | %e A346741 | V |-------|---------|-----|-------|---------|-----------|-------------| %e A346741 | I | 4 | A069705 | | | | 1 2 4 | 1 2 4 | %e A346741 | S | | A000034 | | | | 1 2 | 1 2 | %e A346741 | O | | A000012 | | | | 1 | 1 | %e A346741 | R |-------|---------|-----|-------|---------|-----------|-------------| %e A346741 | S | 5 | A010686 | | | | | 1 5 | %e A346741 | | | A010684 | | | | | 1 3 | %e A346741 | | | A000034 | | | | | 1 2 | %e A346741 | | | A000012 | | | | | 1 | %e A346741 | | | A000012 | | | | | 1 | %e A346741 |---|-------|---------|-----|-------|---------|-----------|-------------| %e A346741 . %e A346741 In the above table both the zone of partitions and the "Link" zone are the same zones as in the table of the example section of A338156, but here in the lower zone the divisors are ordered in accordance with the sections of the set of partitions of n. %e A346741 The number of rows in the j-th section of the lower zone is equal to A000041(j-1). %e A346741 The divisors of the j-th section are also the parts of the j-th section of the set of partitions of n. %Y A346741 Another version of A338156. %Y A346741 Row n has length A006128(n). %Y A346741 The sum of row n is A066186(n). %Y A346741 The product of row n is A007870(n). %Y A346741 Row n lists the first n rows of A336812. %Y A346741 The number of parts k in row n is A066633(n,k). %Y A346741 The sum of all parts k in row n is A138785(n,k). %Y A346741 The number of parts >= k in row n is A181187(n,k). %Y A346741 The sum of all parts >= k in row n is A206561(n,k). %Y A346741 The number of parts <= k in row n is A210947(n,k). %Y A346741 The sum of all parts <= k in row n is A210948(n,k). %Y A346741 Cf. A000012, A000034, A000041, A000070, A002260, A010684, A010686, A027750, A066633, A069705, A135010, A138785, A181187, A221529, A221649, A237593, A302246, A302247, A336811, A340011, A340031, A340032, A340035, A340056, A340057. %K A346741 nonn,tabf %O A346741 1,4 %A A346741 _Omar E. Pol_, Jul 31 2021