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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.

%I A345116 #24 Jun 10 2021 01:53:48
%S A345116 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 A345116 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 A345116 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 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.
%C A345116 Row n lists the terms of the n-th row of A333516 in nonincreasing order.
%C A345116 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 A345116 Triangle begins:
%e A345116 1;
%e A345116 2, 1, 1;
%e A345116 3, 2, 2, 1, 1, 1;
%e A345116 4, 3, 3, 2, 2, 2, 1, 1, 1, 1;
%e A345116 5, 4, 4, 3, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1;
%e A345116 6, 5, 5, 4, 4, 4, 3, 3, 3, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1;
%e A345116 ...
%e A345116 For n = 6 the divisors of the terms of the 6th row of triangle are:
%e A345116 6, 5, 5, 4, 4, 4, 3, 3, 3, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1;
%e A345116 3, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1;
%e A345116 2,       1, 1, 1;
%e A345116 1;
%e A345116 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 A345116 Mirror of A110730.
%Y A345116 Row lengths gives A000217, n >= 1.
%Y A345116 Row sums gives A000292, n >= 1.
%Y A345116 Every column gives A000027.
%Y A345116 Cf. A000203, A175254, A237593, A245092, A333516, A340581.
%K A345116 nonn,tabf
%O A345116 1,2
%A A345116 _Omar E. Pol_, Jun 08 2021