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%I #11 Oct 14 2021 11:07:54
%S 1,1,2,1,2,3,1,2,3,4,1,2,2,4,5,1,2,3,2,5,6,1,2,3,4,3,6,7,1,2,2,2,5,2,
%T 7,8,1,2,3,2,2,6,5,8,9,1,2,3,2,3,6,7,2,9,10,1,2,2,4,3,2,3,8,4,10,11,1,
%U 2,3,4,5,3,5,2,9,3,11,12,1,2,3,2,3,6,2,2,2,10,7,12,13,1,2,2,2,2,2,7,2,4,2,11,2,13,14
%N Square array A(n,k) = the nearest common ancestor of n and n*k in Doudna tree (A005940).
%C Array is read by falling 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) = A348041(n, n*k).
%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 | 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
%e 3 | 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 3, 3, 3,
%e 4 | 4, 4, 2, 4, 2, 2, 2, 4, 4, 2, 2, 2, 2, 2, 2, 4, 2,
%e 5 | 5, 5, 3, 5, 2, 3, 3, 5, 3, 2, 5, 3, 5, 3, 2, 5, 5,
%e 6 | 6, 6, 2, 6, 6, 2, 3, 6, 2, 6, 3, 2, 3, 3, 6, 6, 3,
%e 7 | 7, 7, 5, 7, 3, 5, 2, 7, 5, 3, 3, 5, 5, 2, 3, 7, 7,
%e 8 | 8, 8, 2, 8, 2, 2, 2, 8, 4, 2, 2, 2, 2, 2, 2, 8, 2,
%e 9 | 9, 9, 4, 9, 2, 4, 2, 9, 4, 2, 2, 4, 2, 2, 2, 9, 2,
%e 10 | 10, 10, 3, 10, 2, 3, 3, 10, 3, 2, 10, 3, 5, 3, 2, 10, 5,
%e 11 | 11, 11, 7, 11, 5, 7, 3, 11, 7, 5, 2, 7, 3, 3, 5, 11, 5,
%e 12 | 12, 12, 2, 12, 6, 2, 3, 12, 2, 6, 3, 2, 3, 3, 12, 12, 3,
%e 13 | 13, 13, 11, 13, 7, 11, 5, 13, 11, 7, 3, 11, 2, 5, 7, 13, 3,
%e 14 | 14, 14, 5, 14, 3, 5, 2, 14, 5, 3, 3, 5, 5, 2, 3, 14, 14,
%e 15 | 15, 15, 6, 15, 2, 6, 15, 15, 6, 2, 3, 6, 3, 15, 2, 15, 3,
%e 16 | 16, 16, 2, 16, 2, 2, 2, 16, 4, 2, 2, 2, 2, 2, 2, 16, 2,
%e 17 | 17, 17, 13, 17, 11, 13, 7, 17, 13, 11, 5, 13, 3, 7, 11, 17, 2,
%o (PARI)
%o \\ Needs also code from A348041:
%o A348043sq(x,y) = A348041sq(x,x*y);
%o A348043list(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] = A348043sq(col,(a-(col-1))))); (v); };
%o v348043 = A348043list(up_to);
%o A348043(n) = v348043[n];
%Y Cf. A005940, A156552, A348041, A348042, A348044 (main diagonal).
%Y Cf. A000027 (all columns k that are powers of two: k = 2^e, for e >= 0).
%K nonn,tabl
%O 1,3
%A _Antti Karttunen_, Sep 27 2021
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