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