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 A340746 #26 Jan 22 2022 08:41:52
%S A340746 24,40,60,67,88,100,132,136,147,150,184,204,220,227,232,276,307,323,
%T A340746 328,330,340,348,367,376,387,424,460,472,484,492,499,510,547,550,564,
%U A340746 567,568,580,627,636,664,675,690,707,708,712,726,748,767
%N A340746 Numbers in array A322744 that do not have a unique decomposition into numbers of A307002 and are not equal to A322744(n,k), n > 1, k in the sequence.
%C A340746 While array A322744 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 A340746 The numbers in this sequence are primitive in the sense that they are not A322744 multiples of an earlier number in the sequence.
%e A340746 24 = A322744(4,4). Also 24 = A322744(6,3) and 24 = A322744(2,8). These two decompositions are the same but they differ from A322744(4,4) as follows. 6 = A322744(2,2) and 8 = A322744(2,3), making 24 = A322744(A322744(2,2), 3) and 24 = A322744(2, A322744(2,3)). Thus 24 can be written as A322744(2,2,3), a well-defined composition because A322744(n,k) is associative. 2,3 and 4 are in A307002, thus A322744(4,4) and A322744(2,2,3) are different decompositions of 24, so 24 is in the sequence.
%e A340746 40 is in the sequence because 40 = A322744(3,10) = A322744(4,7) and 3,4,7 and 10 are in A307002.
%e A340746 67 is in the sequence because 67 = A322744(3,17) = A322744(7,7) and 3,7 and 17 are in A307002.
%e A340746 220 has three decompositions. 220 = A322744(4,37) = A322744(7,22) = A322744(10,15) and 4,7,10,15,22 and 37 are in A307002.
%e A340746 72 = A322744(2,2,2,3) = A322744(2,4,4) is not in the sequence because 72 = A322744(2,24) and 24 is in the sequence.
%t A340746 T[n_,k_]:=T[n,k]=(3*n*k-If[OddQ@n,If[OddQ@k,n+k-1,k],If[OddQ@k,n,0]])/2;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&&ContainsNone[list,Flatten@F@i],AppendTo[list,i]],{i,500}];list (* _Giorgos Kalogeropoulos_, Apr 11 2021 *)
%Y A340746 Cf. A307002, A322744, A340747.
%K A340746 nonn
%O A340746 1,1
%A A340746 _David Lovler_, Jan 18 2021