A372053 Irregular array read by rows: Row n lists the factorizations of n into a product of nondecreasing integers >= 2.

2, 3, 2, 2, 4, 5, 2, 3, 6, 7, 2, 2, 2, 2, 4, 8, 3, 3, 9, 2, 5, 10, 11, 2, 2, 3, 2, 6, 3, 4, 12, 13, 2, 7, 14, 3, 5, 15, 2, 2, 2, 2, 2, 2, 4, 2, 8, 4, 4, 16, 17, 2, 3, 3, 2, 9, 3, 6, 18, 19, 2, 2, 5, 2, 10, 4, 5, 20, 3, 7, 21, 2, 11, 22, 23, 2, 2, 2, 3, 2, 2, 6, 2, 3, 4, 2, 12, 3, 8, 4, 6, 24, 5, 5, 25, 2, 13, 26, 3, 3, 3, 3, 9, 27, 2, 2, 7, 2, 14, 4, 7, 28, 29, 2, 3, 5, 2, 15, 3, 10, 5, 6, 30

Offset

2,1

Links

Michael De Vlieger, Table of n, a(n) for n = 2..19795 (rows n = 1..1000, flattened)

Example

The factorizations of the numbers 2 through 24 are:
2;
3;
2, 2; 4;
5;
2, 3; 6;
7;
2, 2, 2; 2, 4; 8;
3, 3; 9;
2, 5; 10;
11;
2, 2, 3; 2, 6; 3, 4; 12;
13;
2, 7; 14;
3, 5; 15;
2, 2, 2, 2; 2, 2, 4; 2, 8; 4, 4; 16;
17;
2, 3, 3; 2, 9; 3, 6; 18;
19;
2, 2, 5; 2, 10; 4, 5; 20;
3, 7; 21;
2, 11; 22;
23;
2, 2, 2, 3; 2, 2, 6; 2, 3, 4; 2, 12; 3, 8; 4, 6; 24;

Mathematica

f[x_] := If[x <= 1, {{}}, Join @@ Table[Map[Prepend[#, d] &, Select[f[x/d], Min @@ # >= d &]], {d, Rest@ Divisors[x]}]]; Array[Flatten @* f, 29, 2]] // Flatten (* Michael De Vlieger, Apr 22 2024 *)

Crossrefs

Sequence in context: A287707 A029247 A194020 * A372048 A053269 A163873

Adjacent sequences: A372050 A372051 A372052 * A372054 A372055 A372056

Keyword

nonn,tabf

Author

N. J. A. Sloane, Apr 22 2024, following a suggestion from Scott R. Shannon

Extensions

The DATA section is longer than usual in order to show the factorizations of 30.

Status

approved