A384223 -id:A384223 - 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.

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, 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, 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

Offset: 1

Omar E. Pol, Jun 04 2025

If n is odd then row n lists A000005(n) 1's.
If n is a power of 2 then row n is 1 plus the exponent of the power of 2.
See A384222 for a more detailed example (with a different rule for sublists).

			Triangle begins:
  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;
  ...
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.

Row sums give A000005.
Row lengths give A001227.
Companion of A384223.
Cf. A000079, A027750, A237270, A237271, A237593, A279387, A384222.

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.

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