cp's OEIS Frontend

A340530 Irregular triangle read by rows T(n,k) in which row n has length is A000070(n-1) and every column k is A006218, (n >= 1, k >= 1).

%I A340530 #19 Jun 01 2025 17:41:00
%S A340530 1,3,1,5,3,1,1,8,5,3,3,1,1,1,10,8,5,5,3,3,3,1,1,1,1,1,14,10,8,8,5,5,5,
%T A340530 3,3,3,3,3,1,1,1,1,1,1,1,16,14,10,10,8,8,8,5,5,5,5,5,3,3,3,3,3,3,3,1,
%U A340530 1,1,1,1,1,1,1,1,1,1,20,16,14,14,10,10,10,8,8,8,8,8,5,5,5,5,5,5,5
%N A340530 Irregular triangle read by rows T(n,k) in which row n has length is A000070(n-1) and every column k is A006218, (n >= 1, k >= 1).
%C A340530 The sum of row n equals A284870(n), the total number of parts in all partitions of all positive integers <= n. It is conjectured that this property is due to the correspondence between divisors and partitions. For more information see A336811.
%F A340530 a(m) = A006218(A176206(m)), assuming A176206 has offset 1.
%F A340530 T(n,k) = A006218(A176206(n,k)), assuming A176206 has offset 1.
%e A340530 Triangle begins:
%e A340530    1;
%e A340530    3,  1;
%e A340530    5,  3,  1,  1;
%e A340530    8,  5,  3,  3, 1, 1, 1;
%e A340530   10,  8,  5,  5, 3, 3, 3, 1, 1, 1, 1, 1;
%e A340530   14, 10,  8,  8, 5, 5, 5, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1;
%e A340530 ...
%e A340530 For n = 5 the length of row 5 is A000070(4) = 12.
%e A340530 The sum of row 5 is 10 + 8 + 5 + 5 + 3 + 3 + 3 + 1 + 1 + 1 + 1 + 1 = 42, equaling A284870(5).
%Y A340530 Row sums give A284870.
%Y A340530 Cf. A340526 (a regular version).
%Y A340530 Members of the same family are: A176206, A337209, A339258, A340531.
%Y A340530 Cf. A339278, A339304, A340423, A340529.
%Y A340530 Cf. A000070, A006128, A336811.
%K A340530 nonn,tabf
%O A340530 1,2
%A A340530 _Omar E. Pol_, Jan 10 2021