A345116 Irregular triangle T(n,k) read by rows in which row n has length the n-th triangular number A000217(n) and every column k lists the positive integers A000027, n >= 1, k >= 1.

1, 2, 1, 1, 3, 2, 2, 1, 1, 1, 4, 3, 3, 2, 2, 2, 1, 1, 1, 1, 5, 4, 4, 3, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 6, 5, 5, 4, 4, 4, 3, 3, 3, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 7, 6, 6, 5, 5, 5, 4, 4, 4, 4, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 8, 7, 7, 6, 6, 6, 5, 5, 5, 5

Offset: 1

Author

Omar E. Pol, Jun 08 2021

Keywords

• nonn
• tabf

Comments

Row n lists the terms of the n-th row of A333516 in nonincreasing order.

The sum of the divisors of the terms of the n-th row of the triangle is equal to A175254(n), equaling the volume of the stepped pyramid with n levels described in A245092.

Examples

			Triangle begins:
1;
2, 1, 1;
3, 2, 2, 1, 1, 1;
4, 3, 3, 2, 2, 2, 1, 1, 1, 1;
5, 4, 4, 3, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1;
6, 5, 5, 4, 4, 4, 3, 3, 3, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1;
...
For n = 6 the divisors of the terms of the 6th row of triangle are:
6, 5, 5, 4, 4, 4, 3, 3, 3, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1;
3, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1;
2,       1, 1, 1;
1;
The sum of these divisors is equal to A175254(6) = 82, equaling the volume of the stepped pyramid with six levels described in A245092.
		

Crossrefs

Mirror of A110730.

Row lengths gives A000217, n >= 1.

Row sums gives A000292, n >= 1.

Every column gives A000027.

Cf. A000203, A175254, A237593, A245092, A333516, A340581.