A348042 Square array A(n,k) = the nearest common ancestor of n, k and n*k in Doudna tree (A005940).

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, 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, 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

Offset

1,5

Comments

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), ...

Links

Table of n, a(n) for n=1..105.

Index entries for sequences computed from indices in prime factorization

Formula

A(n, k) = A(k, n).

A(n, k) = A348041(n*k, A348041(n, k)).

A(n, k) = A348041(n, A348043(k, n)) = A348041(k, A348043(n, k)).

For any two squares s=u^2 and t=v^2, A(s, t) is a square also.

Example

The top left 17x17 corner of the array:
  n/k |  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17
------+-------------------------------------------------------------
    1 |  1, 1, 1, 1, 1, 1, 1, 1, 1,  1,  1,  1,  1,  1,  1,  1,  1,
    2 |  1, 2, 2, 2, 2, 2, 2, 2, 2,  2,  2,  2,  2,  2,  2,  2,  2,
    3 |  1, 2, 2, 2, 3, 2, 3, 2, 2,  3,  3,  2,  3,  3,  3,  2,  3,
    4 |  1, 2, 2, 4, 2, 2, 2, 4, 4,  2,  2,  2,  2,  2,  2,  4,  2,
    5 |  1, 2, 3, 2, 2, 3, 3, 2, 2,  2,  5,  3,  5,  3,  2,  2,  5,
    6 |  1, 2, 2, 2, 3, 2, 3, 2, 2,  3,  3,  2,  3,  3,  6,  2,  3,
    7 |  1, 2, 3, 2, 3, 3, 2, 2, 2,  3,  3,  3,  5,  2,  3,  2,  7,
    8 |  1, 2, 2, 4, 2, 2, 2, 8, 4,  2,  2,  2,  2,  2,  2,  8,  2,
    9 |  1, 2, 2, 4, 2, 2, 2, 4, 4,  2,  2,  2,  2,  2,  2,  4,  2,
   10 |  1, 2, 3, 2, 2, 3, 3, 2, 2,  2,  5,  3,  5,  3,  2,  2,  5,
   11 |  1, 2, 3, 2, 5, 3, 3, 2, 2,  5,  2,  3,  3,  3,  3,  2,  5,
   12 |  1, 2, 2, 2, 3, 2, 3, 2, 2,  3,  3,  2,  3,  3,  6,  2,  3,
   13 |  1, 2, 3, 2, 5, 3, 5, 2, 2,  5,  3,  3,  2,  5,  3,  2,  3,
   14 |  1, 2, 3, 2, 3, 3, 2, 2, 2,  3,  3,  3,  5,  2,  3,  2,  7,
   15 |  1, 2, 3, 2, 2, 6, 3, 2, 2,  2,  3,  6,  3,  3,  2,  2,  3,
   16 |  1, 2, 2, 4, 2, 2, 2, 8, 4,  2,  2,  2,  2,  2,  2, 16,  2,
   17 |  1, 2, 3, 2, 5, 3, 7, 2, 2,  5,  5,  3,  3,  7,  3,  2,  2,

Prog

(PARI)
\\ Needs also code from A348041:
up_to = 105;
A348042sq(row, col) = A348041sq(row*col, A348041sq(row, col));
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); };
v348042 = A348042list(up_to);
A348042(n) = v348042[n];

Crossrefs

Cf. A005940, A156552, A348041, A348043, A348044 (main diagonal).

Sequence in context: A154325 A129765 A143187 * A143209 A163994 A355802

Adjacent sequences: A348039 A348040 A348041 * A348043 A348044 A348045

Keyword

nonn,tabl

Author

Antti Karttunen, Sep 27 2021

Status

approved