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

1,3

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

Links

Table of n, a(n) for n=1..82.

Example

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;
  ...

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 *)

Crossrefs

Subsequence of A027750.

Row sums give A379384.

Odd terms give A379288.

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

Sequence in context: A355634 A394673 A275280 * A319845 A319847 A334217

Adjacent sequences: A379371 A379372 A379373 * A379375 A379376 A379377

Keyword

nonn,tabf

Author

Omar E. Pol, Dec 21 2024

Extensions

More terms from Alois P. Heinz, Dec 21 2024

Status

approved