OFFSET
1,4
COMMENTS
Also due to the correspondence divisor/part row n lists the terms of the n-th row of A338156 in nondecreasing order. In other words: row n lists in nondecreasing order the divisors of the terms of the n-th row of A176206. - Omar E. Pol, Jun 16 2022
LINKS
Paolo Xausa, Table of n, a(n) for n = 1..9687, (rows 1..18 of triangle, flattened)
EXAMPLE
Triangle begins:
1;
1,1,2;
1,1,1,1,2,3;
1,1,1,1,1,1,1,2,2,2,3,4;
1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,3,3,4,5;
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,4,4,5,6;
...
For n = 4 the partitions of 4 are [4], [2, 2], [3, 1], [2, 1, 1], [1, 1, 1, 1]. There are seven 1's, three 2's, only one 3 and only one 4, so the 4th row of this triangle is [1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 4].
On the other hand for n = 4 the 4th row of A176206 is [4, 3, 2, 2, 1, 1, 1] and the divisors of these terms are [1, 2, 4], [1, 3], [1, 2], [1, 2], [1], [1], [1] the same as the 4th row of A338156. These divisors listed in nondecreasing order give the 4th row of this triangle. - Omar E. Pol, Jun 16 2022
MATHEMATICA
nrows=10; Array[Sort[Flatten[IntegerPartitions[#]]]&, nrows] (* Paolo Xausa, Jun 16 2022 *)
PROG
(PARI) row(n) = my(list = List()); forpart(p=n, for (k=1, #p, listput(list, p[k])); ); vecsort(Vec(list)); \\ Michel Marcus, Jun 16 2022
CROSSREFS
Mirror of A302246.
Row n has length A006128(n).
The sum of row n is A066186(n).
The number of parts k in row n is A066633(n,k).
The sum of all parts k in row n is A138785(n,k).
The number of parts >= k in row n is A181187(n,k).
The sum of all parts >= k in row n is A206561(n,k).
The number of parts <= k in row n is A210947(n,k).
The sum of all parts <= k in row n is A210948(n,k).
KEYWORD
nonn,tabf
AUTHOR
Omar E. Pol, Apr 05 2018
STATUS
approved