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.

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, 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, 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

Offset

1,2

Comments

All divisors of all terms of n-th row are also all parts of the last section of the set of partitions of n.

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.

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

Links

Paolo Xausa, Table of n, a(n) for n = 1..11732 (rows 1..27 of triangle, flattened)

Example

Triangle begins:
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, 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;
...

Mathematica

A341049[rowmax_]:=Table[Flatten[Table[ConstantArray[n-m, PartitionsP[m]-PartitionsP[m-1]], {m, n-1, 0, -1}]], {n, rowmax}];
A341049[10] (* Generates 10 rows *) (* Paolo Xausa, Feb 17 2023 *)

Prog

(PARI)
A341049(rowmax)=vector(rowmax, n, concat(vector(n, m, vector(numbpart(n-m)-numbpart(n-m-1), i, m))));
A341049(10) \\ Generates 10 rows - Paolo Xausa, Feb 17 2023

Crossrefs

Mirror of A336811.

Row n has length A000041(n-1).

Row sums give A000070.

Right border gives A000027.

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

Sequence in context: A089384 A365138 A228812 * A144113 A370329 A304038

Adjacent sequences: A341046 A341047 A341048 * A341050 A341051 A341052

Keyword

nonn,tabf

Author

Omar E. Pol, Feb 04 2021

Status

approved