cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A330997 Sorted list containing the least number with each possible nonzero number of factorizations into distinct factors > 1.

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%I A330997 #5 Jan 07 2020 09:08:48
%S A330997 1,6,12,24,48,60,64,96,120,144,180,210,216,240,256,288,360,384,420,
%T A330997 432,480,512,720,840,864,900,960,1080,1152,1260,1296,1440,1536,1680,
%U A330997 1728,1800,2048,2160,2304,2310,2520,2592,2880,3072,3360,3456,3600,3840,4320
%N A330997 Sorted list containing the least number with each possible nonzero number of factorizations into distinct factors > 1.
%e A330997 The strict factorizations of a(n) for n = 1..9.
%e A330997   {}  6    12   24     48     60      64     96      120
%e A330997       2*3  2*6  3*8    6*8    2*30    2*32   2*48    2*60
%e A330997            3*4  4*6    2*24   3*20    4*16   3*32    3*40
%e A330997                 2*12   3*16   4*15    2*4*8  4*24    4*30
%e A330997                 2*3*4  4*12   5*12           6*16    5*24
%e A330997                        2*3*8  6*10           8*12    6*20
%e A330997                        2*4*6  2*5*6          2*6*8   8*15
%e A330997                               3*4*5          3*4*8   10*12
%e A330997                               2*3*10         2*3*16  3*5*8
%e A330997                                              2*4*12  4*5*6
%e A330997                                                      2*3*20
%e A330997                                                      2*4*15
%e A330997                                                      2*5*12
%e A330997                                                      2*6*10
%e A330997                                                      3*4*10
%e A330997                                                      2*3*4*5
%t A330997 nn=1000;
%t A330997 strfacs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[strfacs[n/d],Min@@#>d&]],{d,Rest[Divisors[n]]}]];
%t A330997 nds=Length/@Array[strfacs,nn];
%t A330997 Table[Position[nds,i][[1,1]],{i,First/@Gather[nds]}]
%Y A330997 All terms belong to A025487.
%Y A330997 Strict factorizations are A045778, with image A045779.
%Y A330997 The unsorted version is A045780.
%Y A330997 The non-strict version is A330972.
%Y A330997 The least number with n strict factorizations is A330974.
%Y A330997 Cf. A001055, A001222, A033833, A045782, A318286, A325238, A330935, A330973, A330975.
%K A330997 nonn
%O A330997 1,2
%A A330997 _Gus Wiseman_, Jan 06 2020