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 A348824 #23 Jan 27 2022 07:59:39
%S A348824 32,48,72,96,112,126,128,144,160,168,176,192,198,221,224,240,252,256,
%T A348824 264,288,294,304,336,342,347,352,360,368,384,392,396,414,416,432,448,
%U A348824 456,462,480,496,504,512,528,544,545,552,558,560,576,588,599
%N A348824 Numbers in array A327259 that do not have a unique decomposition into numbers of A327261.
%C A348824 While array A327259 has many properties of the multiplication table, one way the numbers that sieve out of the array fail to be prime numbers is that unique factorization does not hold. Some numbers have two or more decompositions.
%C A348824 For i >= 2, A327259(i, a(n)) is in the sequence.
%H A348824 Michael De Vlieger, <a href="/A348824/b348824.txt">Table of n, a(n) for n = 1..1256</a> (all terms m <= 10000)
%H A348824 David Lovler, <a href="/A348824/a348824_1.txt">Decomposition of a(n) into A327261(k)</a>
%e A348824 48 is in the sequence because 48 = A327259(2,12) = A327259(4,6) and 2, 4, 6 and 12 are in A327261.
%e A348824 72 is in the sequence because 72 = A327259(2,2,5) = A327259(6,6) and 2, 5 and 6 are in A327261. A327259(2,2,5) is well-defined because A327259(n,k) is associative.
%e A348824 221 is in the sequence because 221 = A327259(5,25) = A327259(11,11) and 5, 11 and 25 are in A327261.
%e A348824 462 is in the sequence because 462 = A327259(6,39) = A327259(11,22) = A327259(14,17) and 6, 11, 14, 17, 22 and 39 are in A327261.
%e A348824 The first six terms and their decompositions:
%e A348824 1 32 = A327259(2,2,2) = A327259(4,4)
%e A348824 2 48 = A327259(2,12) = A327259(4,6)
%e A348824 3 72 = A327259(2,2,5) = A327259(6,6)
%e A348824 4 96 = A327259(2,2,6) = A327259(4,12)
%e A348824 5 112 = A327259(2,28) = A327259(4,14)
%e A348824 6 126 = A327259(5,14) = A327259(6,11)
%e A348824 More in a-file.
%t A348824 T[n_,k_]:=2n*k-If[Mod[n,2]==1,If[Mod[k,2]==1,n+k-1,k],If[Mod[k,2]==1,n,0]];F[d_]:=If[(q=Union[Sort/@(Position[Table[T[n,k],{n,2,Ceiling[d/3]},{k,2,Ceiling[d/3]}],d]+1)])=={},{{d}},q];FC[x_]:=FixedPoint[Union[Sort/@Flatten[Flatten/@Tuples[#]&/@((F/@#&/@#)&[#]),1]]&,F[x]];list={};Do[If[Length@FC@i>1,AppendTo[list,i]],{i,300}];list (* _Giorgos Kalogeropoulos_, Nov 05 2021 *)
%Y A348824 Cf. A327259, A327261, A340747.
%K A348824 nonn
%O A348824 1,1
%A A348824 _David Lovler_, Oct 31 2021
%E A348824 Name amended by _David Lovler_, Jan 26 2022