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 A119646 #16 Jan 08 2023 12:25:12
%S A119646 1,1,1,1,1,1,1,1,1,1,2,2,1,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
%T A119646 2,2,3,2,2,2,2,2,3,2,2,2,3,2,2,2,3,2,2,2,2,2,2,2,2,3,2,3,3,2,2,2,2,3,
%U A119646 3,2,2,3,3,3,3,3,3,2,3,3,3,3,3,2,3,3,3,3,3,3,3,3,3,2,3,3,3,3,3,2,3,3,3,3,3,3
%N A119646 a(n) = maximum number of partitions of n into 3 parts, each having the same product.
%e A119646 a(3)=1, because there is only one way to partition 3.
%e A119646 a(13)=2, because 13 = 6+6+1 = 9+2+2 and 6*6*1 = 9*2*2 = 36.
%e A119646 a(39)=3, because 39 = 20+15+4 = 24+10+5 = 25+8+6 and 20*15*4 = 24*10*5 = 25*8*6 = 1200.
%e A119646 See A103277 for more examples.
%t A119646 pdt[lst_] := lst[[1]]*lst[[2]]*lst[[3]];
%t A119646 tanya[n_] := Max[Length /@ Split[Sort[pdt /@ Union[ Partition[Last /@ Flatten[ FindInstance[a + b + c == n && a >= b >= c > 0, {a, b, c}, Integers,(* failsafe *) Round[n^2/12]]], 3]] ]]];
%t A119646 Table[ tanya@n, {n, 4, 108}]
%t A119646 Table[SortBy[Tally[Times@@@IntegerPartitions[n,{3}]],Last][[-1,2]],{n,3,110}] (* _Harvey P. Dale_, Jan 08 2023 *)
%Y A119646 Cf. A103277, A119028.
%K A119646 nonn
%O A119646 3,11
%A A119646 Joseph Biberstine (jrbibers(AT)indiana.edu) and _Robert G. Wilson v_, Jul 27 2006
%E A119646 Name clarified by _Dmitry Kamenetsky_, Aug 02 2015