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 A348042 #12 Oct 14 2021 11:07:36
%S A348042 1,1,1,1,2,1,1,2,2,1,1,2,2,2,1,1,2,2,2,2,1,1,2,3,4,3,2,1,1,2,2,2,2,2,
%T A348042 2,1,1,2,3,2,2,2,3,2,1,1,2,2,2,3,3,2,2,2,1,1,2,2,4,3,2,3,4,2,2,1,1,2,
%U A348042 3,4,2,3,3,2,4,3,2,1,1,2,3,2,2,2,2,2,2,2,3,2,1,1,2,2,2,2,2,2,2,2,2,2,2,2,1
%N A348042 Square array A(n,k) = the nearest common ancestor of n, k and n*k in Doudna tree (A005940).
%C A348042 Array is symmetric and is read by antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ...
%H A348042 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A348042 A(n, k) = A(k, n).
%F A348042 A(n, k) = A348041(n*k, A348041(n, k)).
%F A348042 A(n, k) = A348041(n, A348043(k, n)) = A348041(k, A348043(n, k)).
%F A348042 For any two squares s=u^2 and t=v^2, A(s, t) is a square also.
%e A348042 The top left 17x17 corner of the array:
%e A348042 n/k | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
%e A348042 ------+-------------------------------------------------------------
%e A348042 1 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
%e A348042 2 | 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
%e A348042 3 | 1, 2, 2, 2, 3, 2, 3, 2, 2, 3, 3, 2, 3, 3, 3, 2, 3,
%e A348042 4 | 1, 2, 2, 4, 2, 2, 2, 4, 4, 2, 2, 2, 2, 2, 2, 4, 2,
%e A348042 5 | 1, 2, 3, 2, 2, 3, 3, 2, 2, 2, 5, 3, 5, 3, 2, 2, 5,
%e A348042 6 | 1, 2, 2, 2, 3, 2, 3, 2, 2, 3, 3, 2, 3, 3, 6, 2, 3,
%e A348042 7 | 1, 2, 3, 2, 3, 3, 2, 2, 2, 3, 3, 3, 5, 2, 3, 2, 7,
%e A348042 8 | 1, 2, 2, 4, 2, 2, 2, 8, 4, 2, 2, 2, 2, 2, 2, 8, 2,
%e A348042 9 | 1, 2, 2, 4, 2, 2, 2, 4, 4, 2, 2, 2, 2, 2, 2, 4, 2,
%e A348042 10 | 1, 2, 3, 2, 2, 3, 3, 2, 2, 2, 5, 3, 5, 3, 2, 2, 5,
%e A348042 11 | 1, 2, 3, 2, 5, 3, 3, 2, 2, 5, 2, 3, 3, 3, 3, 2, 5,
%e A348042 12 | 1, 2, 2, 2, 3, 2, 3, 2, 2, 3, 3, 2, 3, 3, 6, 2, 3,
%e A348042 13 | 1, 2, 3, 2, 5, 3, 5, 2, 2, 5, 3, 3, 2, 5, 3, 2, 3,
%e A348042 14 | 1, 2, 3, 2, 3, 3, 2, 2, 2, 3, 3, 3, 5, 2, 3, 2, 7,
%e A348042 15 | 1, 2, 3, 2, 2, 6, 3, 2, 2, 2, 3, 6, 3, 3, 2, 2, 3,
%e A348042 16 | 1, 2, 2, 4, 2, 2, 2, 8, 4, 2, 2, 2, 2, 2, 2, 16, 2,
%e A348042 17 | 1, 2, 3, 2, 5, 3, 7, 2, 2, 5, 5, 3, 3, 7, 3, 2, 2,
%o A348042 (PARI)
%o A348042 \\ Needs also code from A348041:
%o A348042 up_to = 105;
%o A348042 A348042sq(row,col) = A348041sq(row*col,A348041sq(row,col));
%o A348042 A348042list(up_to) = { my(v = vector(up_to), i=0); for(a=1,oo, for(col=1,a, i++; if(i > up_to, return(v)); v[i] = A348042sq(col,(a-(col-1))))); (v); };
%o A348042 v348042 = A348042list(up_to);
%o A348042 A348042(n) = v348042[n];
%Y A348042 Cf. A005940, A156552, A348041, A348043, A348044 (main diagonal).
%K A348042 nonn,tabl
%O A348042 1,5
%A A348042 _Antti Karttunen_, Sep 27 2021