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

1,2

Comments

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.

Links

Paolo Xausa, Table of n, a(n) for n = 1..13282 (rows 1..3000 of triangle, flattened).

Example

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.

Mathematica

A384224row[n_] := Map[Length, Split[Divisors[n], EvenQ[#2] &]];
Array[A384224row, 50] (* Paolo Xausa, Sep 05 2025 *)

Crossrefs

Row sums give A000005.

Row lengths give A001227.

Companion of A384223.

Cf. A000079, A027750.

Sequence in context: A275699 A305633 A214123 * A396561 A369188 A007862

Adjacent sequences: A384221 A384222 A384223 * A384225 A384226 A384227

Keyword

nonn,tabf,easy

Author

Omar E. Pol, Jun 04 2025

Status

approved