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A331886 T(n, k) is the least positive m such that floor(n/m) = floor(k/m). Square array T(n, k) read by antidiagonals, n >= 0 and k >= 0.

%I A331886 #18 Feb 02 2020 17:52:51
%S A331886 1,2,2,3,1,3,4,3,3,4,5,4,1,4,5,6,5,2,2,5,6,7,6,5,1,5,6,7,8,7,6,3,3,6,
%T A331886 7,8,9,8,7,3,1,3,7,8,9,10,9,8,7,2,2,7,8,9,10,11,10,9,8,4,1,4,8,9,10,
%U A331886 11,12,11,10,9,4,4,4,4,9,10,11,12,13,12,11,10
%N A331886 T(n, k) is the least positive m such that floor(n/m) = floor(k/m). Square array T(n, k) read by antidiagonals, n >= 0 and k >= 0.
%H A331886 Rémy Sigrist, <a href="/A331886/b331886.txt">Table of n, a(n) for n = 0..10010</a> (antidiagonals 0..140)
%H A331886 Rémy Sigrist, <a href="/A331886/a331886.png">Colored representation of T(n, k) for n, k = 0..1000</a> (where the hue is function of T(n, k))
%H A331886 Rémy Sigrist, <a href="/A331886/a331886_1.png">Colored representation of floor(n/T(n, k)) for n, k = 0..1000</a> (where the hue is function of floor(n/T(n, k)), red pixels correspond to 0's)
%F A331886 T(n, k) = T(k, n).
%F A331886 T(n, k) = 1 iff n = k.
%F A331886 T(n, k) <= 1 + max(n, k) with equality iff max(n, k) >= 2*min(n, k).
%F A331886 T(n, n+1) = A007978(n+1).
%e A331886 Array T(n, k) begins:
%e A331886    n\k|   0   1   2   3   4   5   6   7   8   9  10  11  12
%e A331886    ---+----------------------------------------------------
%e A331886      0|   1   2   3   4   5   6   7   8   9  10  11  12  13
%e A331886      1|   2   1   3   4   5   6   7   8   9  10  11  12  13
%e A331886      2|   3   3   1   2   5   6   7   8   9  10  11  12  13
%e A331886      3|   4   4   2   1   3   3   7   8   9  10  11  12  13
%e A331886      4|   5   5   5   3   1   2   4   4   9  10  11  12  13
%e A331886      5|   6   6   6   3   2   1   4   4   5   5  11  12  13
%e A331886      6|   7   7   7   7   4   4   1   2   3   5   6   6  13
%e A331886      7|   8   8   8   8   4   4   2   1   3   5   6   6   7
%e A331886      8|   9   9   9   9   9   5   3   3   1   2   4   4   7
%e A331886      9|  10  10  10  10  10   5   5   5   2   1   3   3   7
%e A331886     10|  11  11  11  11  11  11   6   6   4   3   1   2   5
%e A331886     11|  12  12  12  12  12  12   6   6   4   3   2   1   5
%e A331886     12|  13  13  13  13  13  13  13   7   7   7   5   5   1
%o A331886 (PARI) T(n,k) = for (m=1, oo, if (n\m==k\m, return (m)))
%Y A331886 Cf. A007978, A331902.
%K A331886 nonn,tabl,look
%O A331886 0,2
%A A331886 _Rémy Sigrist_, Jan 30 2020