A379374 Irregular triangle read by rows in which row n lists the divisors of n except the divisors "e" described in A005279.

1, 1, 2, 1, 3, 1, 2, 4, 1, 5, 1, 2, 6, 1, 7, 1, 2, 4, 8, 1, 3, 9, 1, 2, 5, 10, 1, 11, 1, 2, 12, 1, 13, 1, 2, 7, 14, 1, 3, 15, 1, 2, 4, 8, 16, 1, 17, 1, 2, 6, 18, 1, 19, 1, 2, 4, 10, 20, 1, 3, 7, 21, 1, 2, 11, 22, 1, 23, 1, 2, 24, 1, 5, 25, 1, 2, 13, 26, 1, 3, 9, 27

Offset: 1

Author

Omar E. Pol, Dec 21 2024

Keywords

• nonn
• tabf

Comments

Observation: the sequence of the number of odd terms in row n coincides with at least the first 10000 terms of A237271.

The observation is true for all numbers. For a proof see A379288. - Hartmut F. W. Hoft, Jan 25 2025

Examples

			Triangle begins:
  1;
  1,  2;
  1,  3;
  1,  2,  4;
  1,  5;
  1,  2,  6;
  1,  7;
  1,  2,  4,  8;
  1,  3,  9;
  1,  2,  5, 10;
  1, 11;
  1,  2, 12;
  1, 13;
  1,  2,  7, 14;
  1,  3, 15;
  1,  2,  4,  8, 16;
  1, 17;
  1,  2,  6, 18;
  1, 19;
  1,  2,  4, 10, 20;
  ...
		

Crossrefs

Subsequence of A027750.

Row sums give A379384.

Odd terms give A379288.

Cf. A001227, A005279, A010814, A237271, A237593, A239657, A237271, A379379.

Programs

Mathematica

row[n_] := Module[{d = Partition[Divisors[n], 2, 1]}, Join[{1}, Select[d, #[[2]] >= 2*#[[1]] &][[;; , 2]]]]; Table[row[n], {n, 1, 27}] // Flatten (* Amiram Eldar, Dec 22 2024 *)

Extensions

More terms from Alois P. Heinz, Dec 21 2024