A345116 - OEIS

%I #24 Jun 10 2021 01:53:48

%S 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,

%T 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,

%U 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

%N 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.

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

%C 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.

%e Triangle begins:

%e 1;

%e 2, 1, 1;

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

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

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

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

%e ...

%e For n = 6 the divisors of the terms of the 6th row of triangle are:

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

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

%e 2,       1, 1, 1;

%e 1;

%e The sum of these divisors is equal to A175254(6) = 82, equaling the volume of the stepped pyramid with six levels described in A245092.

%Y Mirror of A110730.

%Y Row lengths gives A000217, n >= 1.

%Y Row sums gives A000292, n >= 1.

%Y Every column gives A000027.

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

%K nonn,tabf

%O 1,2

%A _Omar E. Pol_, Jun 08 2021