A341049 - OEIS

%I #25 Feb 17 2023 08:33:22

%S 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 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 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 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 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 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 For further information about the correspondence divisor/part see A338156 and A336812.

%H Paolo Xausa, <a href="/A341049/b341049.txt">Table of n, a(n) for n = 1..11732 (rows 1..27 of triangle, flattened)</a>

%e Triangle begins:

%e 1;

%e 2;

%e 1, 3;

%e 1, 2, 4;

%e 1, 1, 2, 3, 5;

%e 1, 1, 2, 2, 3, 4, 6;

%e 1, 1, 1, 1, 2, 2, 3, 3, 4, 5, 7;

%e 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 5, 6, 8;

%e 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 6, 7, 9;

%e ...

%t A341049[rowmax_]:=Table[Flatten[Table[ConstantArray[n-m,PartitionsP[m]-PartitionsP[m-1]],{m,n-1,0,-1}]],{n,rowmax}];

%t A341049[10] (* Generates 10 rows *) (* _Paolo Xausa_, Feb 17 2023 *)

%o (PARI)

%o A341049(rowmax)=vector(rowmax,n,concat(vector(n,m,vector(numbpart(n-m)-numbpart(n-m-1),i,m))));

%o A341049(10) \\ Generates 10 rows - _Paolo Xausa_, Feb 17 2023

%Y Mirror of A336811.

%Y Row n has length A000041(n-1).

%Y Row sums give A000070.

%Y Right border gives A000027.

%Y Cf. A000070, A000041, A002865, A027750, A028310, A133735, A135010, A138121, A138137, A176206, A182703, A187219, A207378, A237593, A336812, A338156, A339278, A340061.

%K nonn,tabf

%O 1,2

%A _Omar E. Pol_, Feb 04 2021