cp's OEIS Frontend

A384224 Irregular triangle read by rows: T(n,k) is the number of divisors in the k-th sublist of the divisors of n formed by the k-th odd divisor and the next even divisors that are less than the next odd divisor of n, with n >= 1, k >= 1.

%I A384224 #16 Jun 16 2025 17:37:41
%S A384224 1,2,1,1,3,1,1,2,2,1,1,4,1,1,1,2,2,1,1,2,4,1,1,2,2,1,1,1,1,5,1,1,2,2,
%T A384224 2,1,1,3,3,1,1,1,1,2,2,1,1,2,6,1,1,1,2,2,1,1,1,1,3,3,1,1,2,1,3,2,1,1,
%U A384224 6,1,1,1,1,2,2,1,1,1,1,2,3,4,1,1,2,2,1,1,1,1,3,5,1,1,2,2,2,2,1,1,3,3
%N A384224 Irregular triangle read by rows: T(n,k) is the number of divisors in the k-th sublist of the divisors of n formed by the k-th odd divisor and the next even divisors that are less than the next odd divisor of n, with n >= 1, k >= 1.
%C A384224 If n is odd then row n lists A000005(n) 1's.
%C A384224 If n is a power of 2 then row n is 1 plus the exponent of the power of 2.
%C A384224 See A384222 for a more detailed example (with a different rule for sublists).
%e A384224 Triangle begins:
%e A384224   1;
%e A384224   2;
%e A384224   1, 1;
%e A384224   3;
%e A384224   1, 1;
%e A384224   2, 2;
%e A384224   1, 1;
%e A384224   4;
%e A384224   1, 1, 1;
%e A384224   2, 2;
%e A384224   1, 1;
%e A384224   2, 4;
%e A384224   1, 1;
%e A384224   2, 2;
%e A384224   1, 1, 1, 1;
%e A384224   5;
%e A384224   ...
%e A384224 For n = 30 the list of divisors of 30 is [1, 2, 3, 5, 6, 10, 15, 30]. There are four sublists of divisors whose first term is odd. They are [1, 2], [3], [5, 6, 10], [15, 30]. The number of divisors in the sublists are respectively [2, 1, 3, 2], the same as the 30th row of the triangle.
%Y A384224 Row sums give A000005.
%Y A384224 Row lengths give A001227.
%Y A384224 Companion of A384223.
%Y A384224 Cf. A000079, A027750, A237270, A237271, A237593, A279387, A384222.
%K A384224 nonn,tabf,easy
%O A384224 1,2
%A A384224 _Omar E. Pol_, Jun 04 2025