A375037 -id:A375037 - cp's OEIS frontend

A375038 Irregular triangle read by rows T(n,k), n >= 2, k >= 1, in which row n lists the nonmiddle divisors of n.

2, 1, 3, 1, 4, 1, 5, 1, 6, 1, 7, 1, 4, 8, 1, 9, 1, 2, 5, 10, 1, 11, 1, 2, 6, 12, 1, 13, 1, 2, 7, 14, 1, 15, 1, 2, 8, 16, 1, 17, 1, 2, 6, 9, 18, 1, 19, 1, 2, 10, 20, 1, 3, 7, 21, 1, 2, 11, 22, 1, 23, 1, 2, 3, 8, 12, 24, 1, 25, 1, 2, 13, 26, 1, 3, 9, 27, 1, 2, 14, 28

Offset: 2

Omar E. Pol, Jul 28 2024

Except the 1, all positive integers have nonmiddle divisors.

The nonmiddle divisors of n are here the divisors of n that are not in the half-open interval [sqrt(n/2), sqrt(n*2)).

			Triangle begins starting in row n = 2:
  2;
  1, 3;
  1, 4;
  1, 5;
  1, 6;
  1, 7;
  1, 4, 8;
  1, 9;
  1, 2, 5, 10;
  1, 11;
  1, 2, 6, 12;
  ...
For n = 12 the divisors of 12 are [1, 2, 3, 4, 6, 12] and the middle divisors are [3, 4], so the nonmiddle divisors are [1, 2, 6, 12], the same as the row n = 12 of the triangle.

Amiram Eldar, Table of n, a(n) for n = 2..6375 (rows for n = 2..1000, flattened)

Nonzero terms of A375037.
The sum of row n is A302433(n).
The number of terms in row n is A067743(n).
Column 1 gives A054977.
Cf. A027750, A067742, A071090, A299761, A303297.

row[n_] := Select[Divisors[n], !(Sqrt[n/2] <= # < Sqrt[2*n]) &]; Table[row[n], {n, 2, 28}] // Flatten (* Amiram Eldar, Jul 29 2024 *)

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A375038 Irregular triangle read by rows T(n,k), n >= 2, k >= 1, in which row n lists the nonmiddle divisors of n.

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