# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/

Search: id:a330973
Showing 1-1 of 1

%I A330973 #17 Sep 22 2022 11:17:30
%S A330973 1,4,8,12,16,0,24,0,36,0,60,48,0,0,128,72,0,0,96,0,120,256,0,0,0,180,
%T A330973 0,0,144,192,216,0,0,0,0,420,0,240,0,0,0,1024,0,0,384,0,288,0,0,0,0,
%U A330973 360,0,0,0,2048,432,0,0,0,0,0,0,480,0,900,768,0,0,0,0,0
%N A330973 Least positive integer with exactly n factorizations into factors > 1, and 0 if no such number exists.
%H A330973 Robert G. Wilson v, <a href="/A330973/b330973.txt">Table of n, a(n) for n = 1..10000</a>
%H A330973 R. E. Canfield, P. Erdős and C. Pomerance, <a href="http://math.dartmouth.edu/~carlp/PDF/paper39.pdf">On a Problem of Oppenheim concerning "Factorisatio Numerorum"</a>, J. Number Theory 17 (1983), 1-28.
%t A330973 nn=10;
%t A330973 fam[n_]:=fam[n]=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[fam[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
%t A330973 nds=Length/@Array[fam[#]&,2^nn];
%t A330973 Table[If[#=={},0,#[[1,1]]]&[Position[nds,i]],{i,nn}]
%Y A330973 All nonzero terms belong to A025487.
%Y A330973 Includes all highly factorable numbers A033833.
%Y A330973 Factorizations are A001055, with image A045782.
%Y A330973 The version without zeros is A045783.
%Y A330973 The sorted version is A330972.
%Y A330973 The strict version is A330974.
%Y A330973 Positions of zeros are A330976.
%Y A330973 Cf. A001055, A001222, A002033, A007716, A045778, A045779, A330935, A330992, A330997, A330998, A346426.
%K A330973 nonn
%O A330973 1,2
%A A330973 _Gus Wiseman_, Jan 06 2020
%E A330973 More terms from _Jinyuan Wang_, Jul 07 2021

# Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE