来自在线整数百科全书的问候语!http://oeis.org/ Search: id:a033833 Showing 1-1 of 1 %I A033833 %S A033833 1,4,8,12,16,24,36,48,72,96,120,144,192,216,240,288,360,432,480,576, %T A033833 720,960,1080,1152,1440,2160,2880,4320,5040,5760,7200,8640,10080, %U A033833 11520,12960,14400,15120,17280,20160,25920,28800,30240,34560 %N A033833 Highly factorable numbers: numbers with a record number of proper factorizations. %C A033833 First differs from A045783 and A330972 in lacking 60. %C A033833 Indices of records in A028422 or A001055. %H A033833 Amiram Eldar,n,a(n)n=1…235的表(E. R. Canfield等人的术语1…118)%0A0338 33 E. R. Canfield,P. Erd s s,C. Pomerance,关于Factorisatio Numerorum的奥本海姆问题J.数论17(1983)1-28,表1,列“n”。%%H A0338 33 Jun Kyo Kim,关于高可分解数《数论杂志》,第72卷,第1期(1998),第76页91页,第0%A0338 33页,Arnold Knopfmacher和Michael Mays,整数的有序与无序分解,Mathematica杂志,第10卷,第1期(2006),pp.72-89.0%F A0338 33 A00 1055(A(n))=A27 2691(n)。- _Gus Wiseman_, Jan 13 2020 %e A033833 From _Gus Wiseman_, Jan 13 2020: (Start) %e A033833 Factorizations of the initial terms: %e A033833 () (4) (8) (12) (16) (24) (36) (48) %e A033833 (2*2) (2*4) (2*6) (2*8) (3*8) (4*9) (6*8) %e A033833 (2*2*2) (3*4) (4*4) (4*6) (6*6) (2*24) %e A033833 (2*2*3) (2*2*4) (2*12) (2*18) (3*16) %e A033833 (2*2*2*2) (2*2*6) (3*12) (4*12) %e A033833 (2*3*4) (2*2*9) (2*3*8) %e A033833 (2*2*2*3) (2*3*6) (2*4*6) %e A033833 (3*3*4) (3*4*4) %e A033833 (2*2*3*3) (2*2*12) %e A033833 (2*2*2*6) %e A033833 (2*2*3*4) %e A033833 (2*2*2*2*3) %e A033833 (End) %t A033833 nn=100; %t A033833 facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]]; %t A033833 qv=Table[Length[facs[n]],{n,nn}]; %t A033833 Table[Position[qv,i][[1,1]],{i,qv//.{foe___,x_,y_,afe___}/;x>=y:>{foe,x,afe}}] (* _Gus Wiseman_, Jan 13 2020 *) %Y A033833 All terms belong to A025487 as well as to A330972. %Y A033833 The corresponding records are A272691. %Y A033833 The strict version is A331200. %Y A033833 Factorizations are A001055, with image A045782 and complement A330976. %Y A033833 Cf. A028422, A033834, A045778, A045783, A330973, A330998, A331049, A331050. %K A033833 nonn,changed %O A033833 1,2 %A A033833 _Jeff Burch_ # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE