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A341049 Irregular triangle read by rows T(n,k) in which row n lists the terms of n-th row of A336811 in nondecreasing order.

%I A341049 #25 Feb 17 2023 08:33:22
%S A341049 1,2,1,3,1,2,4,1,1,2,3,5,1,1,2,2,3,4,6,1,1,1,1,2,2,3,3,4,5,7,1,1,1,1,
%T A341049 2,2,2,2,3,3,4,4,5,6,8,1,1,1,1,1,1,1,2,2,2,2,3,3,3,3,4,4,5,5,6,7,9,1,
%U A341049 1,1,1,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,4,4,4,4,5,5,6,6,7,8,10
%N A341049 Irregular triangle read by rows T(n,k) in which row n lists the terms of n-th row of A336811 in nondecreasing order.
%C A341049 All divisors of all terms of n-th row are also all parts of the last section of the set of partitions of n.
%C A341049 All divisors of all terms of the first n rows are also all parts of all partitions of n. In other words: all divisors of the first A000070(n-1) terms of the sequence are also all parts of all partitions of n.
%C A341049 For further information about the correspondence divisor/part see A338156 and A336812.
%H A341049 Paolo Xausa, <a href="/A341049/b341049.txt">Table of n, a(n) for n = 1..11732 (rows 1..27 of triangle, flattened)</a>
%e A341049 Triangle begins:
%e A341049 1;
%e A341049 2;
%e A341049 1, 3;
%e A341049 1, 2, 4;
%e A341049 1, 1, 2, 3, 5;
%e A341049 1, 1, 2, 2, 3, 4, 6;
%e A341049 1, 1, 1, 1, 2, 2, 3, 3, 4, 5, 7;
%e A341049 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 5, 6, 8;
%e A341049 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 6, 7, 9;
%e A341049 ...
%t A341049 A341049[rowmax_]:=Table[Flatten[Table[ConstantArray[n-m,PartitionsP[m]-PartitionsP[m-1]],{m,n-1,0,-1}]],{n,rowmax}];
%t A341049 A341049[10] (* Generates 10 rows *) (* _Paolo Xausa_, Feb 17 2023 *)
%o A341049 (PARI)
%o A341049 A341049(rowmax)=vector(rowmax,n,concat(vector(n,m,vector(numbpart(n-m)-numbpart(n-m-1),i,m))));
%o A341049 A341049(10) \\ Generates 10 rows - _Paolo Xausa_, Feb 17 2023
%Y A341049 Mirror of A336811.
%Y A341049 Row n has length A000041(n-1).
%Y A341049 Row sums give A000070.
%Y A341049 Right border gives A000027.
%Y A341049 Cf. A000070, A000041, A002865, A027750, A028310, A133735, A135010, A138121, A138137, A176206, A182703, A187219, A207378, A237593, A336812, A338156, A339278, A340061.
%K A341049 nonn,tabf
%O A341049 1,2
%A A341049 _Omar E. Pol_, Feb 04 2021