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.
%I A272691 #22 Jul 09 2025 04:41:14
%S A272691 1,2,3,4,5,7,9,12,16,19,21,29,30,31,38,47,52,57,64,77,98,105,109,118,
%T A272691 171,212,289,382,392,467,484,662,719,737,783,843,907,1097,1261,1386,
%U A272691 1397,1713,1768,2116,2179,2343,3079,3444,3681,3930,5288,5413,5447
%N A272691 Number of factorizations of the highly factorable numbers A033833.
%C A272691 These are defined as record numbers of factorizations (A001055). - _Gus Wiseman_, Jan 13 2020
%H A272691 Amiram Eldar, <a href="/A272691/b272691.txt">Table of n, a(n) for n = 1..235</a> (terms 1..118 from E. R. Canfield et al.)
%H A272691 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.
%H A272691 Jun Kyo Kim, <a href="https://doi.org/10.1006/jnth.1998.2238">On highly factorable numbers</a>, Journal Of Number Theory, Vol. 72, No. 1 (1998), pp. 76-91.
%F A272691 a(n) = A001055(A033833(n)).
%F A272691 a(n) = A033834(n) + 1. - _Amiram Eldar_, Jun 07 2019
%e A272691 From _Gus Wiseman_, Jan 13 2020: (Start)
%e A272691 The a(1) = 1 through a(8) = 12 factorizations of highly factorable numbers:
%e A272691 () (4) (8) (12) (16) (24) (36) (48)
%e A272691 (2*2) (2*4) (2*6) (2*8) (3*8) (4*9) (6*8)
%e A272691 (2*2*2) (3*4) (4*4) (4*6) (6*6) (2*24)
%e A272691 (2*2*3) (2*2*4) (2*12) (2*18) (3*16)
%e A272691 (2*2*2*2) (2*2*6) (3*12) (4*12)
%e A272691 (2*3*4) (2*2*9) (2*3*8)
%e A272691 (2*2*2*3) (2*3*6) (2*4*6)
%e A272691 (3*3*4) (3*4*4)
%e A272691 (2*2*3*3) (2*2*12)
%e A272691 (2*2*2*6)
%e A272691 (2*2*3*4)
%e A272691 (2*2*2*2*3)
%e A272691 (End)
%t A272691 facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
%t A272691 Table[Length[facs[n]],{n,100}]//.{foe___,x_,y_,afe___}/;x>=y:>{foe,x,afe} (* _Gus Wiseman_, Jan 13 2020 *)
%Y A272691 The strict version is A331232.
%Y A272691 Factorizations are A001055, with image A045782 and complement A330976.
%Y A272691 Highly factorable numbers are A033833, with strict version A331200.
%Y A272691 Cf. A033834, A045778, A045783, A330972, A330973, A330998.
%K A272691 nonn
%O A272691 1,2
%A A272691 _N. J. A. Sloane_, Jun 02 2016, following a suggestion from George Beck