A345272 Irregular triangle read by rows T(n,k) in which row n lists in nonincreasing order all divisors of the terms of the n-th row of triangle A110730, n >= 1, k >= 1.

1, 2, 1, 1, 1, 3, 2, 2, 1, 1, 1, 1, 1, 1, 4, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 4, 4, 3, 3, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 5, 5, 4, 4, 4, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 1

Author

Omar E. Pol, Jun 12 2021

Keywords

• nonn
• tabf

Comments

Note that in the definition A110730 can be replaced with A333516 or with A345116 since these three triangles contain in every row the same terms but in distinct order.

The sum of n-th row is equal to A175254(n) equaling the volume (also the number of cubes) of the stepped pyramid with n levels described in A245092.

Examples

			Triangle begins:
1;
2, 1, 1, 1;
3, 2, 2, 1, 1, 1, 1, 1, 1;
4, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1;
5, 4, 4, 3, 3, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1;
...
For n = 3 the third row of A110730 is [1, 1, 1, 2, 2, 3], so the divisors of these terms in nonincreasing order are [3, 2, 2, 1, 1, 1, 1, 1, 1], the same as the third row of triangle.
		

Crossrefs

Cf. A110730, A175254, A237593, A245092, A333516, A345116.

Programs

PARI

row(n) = my(v=[]); for (k=1, n, for (j=1, n-k+1, v = concat(v, divisors(k)))); vecsort(v,,4); \\ Michel Marcus, Jun 14 2021