|
%I #14 Apr 22 2024 18:29:29
%S 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,
%T 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,
%U 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
%N Irregular array read by rows: Row n lists the factorizations of n into a product of nondecreasing integers >= 2.
%H Michael De Vlieger, <a href="/A372053/b372053.txt">Table of n, a(n) for n = 2..19795</a> (rows n = 1..1000, flattened)
%e The factorizations of the numbers 2 through 24 are:
%e 2;
%e 3;
%e 2, 2; 4;
%e 5;
%e 2, 3; 6;
%e 7;
%e 2, 2, 2; 2, 4; 8;
%e 3, 3; 9;
%e 2, 5; 10;
%e 11;
%e 2, 2, 3; 2, 6; 3, 4; 12;
%e 13;
%e 2, 7; 14;
%e 3, 5; 15;
%e 2, 2, 2, 2; 2, 2, 4; 2, 8; 4, 4; 16;
%e 17;
%e 2, 3, 3; 2, 9; 3, 6; 18;
%e 19;
%e 2, 2, 5; 2, 10; 4, 5; 20;
%e 3, 7; 21;
%e 2, 11; 22;
%e 23;
%e 2, 2, 2, 3; 2, 2, 6; 2, 3, 4; 2, 12; 3, 8; 4, 6; 24;
%t 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 *)
%K nonn,tabf
%O 2,1
%A _N. J. A. Sloane_, Apr 22 2024, following a suggestion from _Scott R. Shannon_
%E The DATA section is longer than usual in order to show the factorizations of 30.
|
