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A331902 T(n, k) = floor(n/m) where m is the least positive integer such that floor(n/m) = floor(k/m). Square array read by antidiagonals, for n >= 0 and k >= 0.

%I A331902 #15 Feb 04 2020 21:25:00
%S A331902 0,0,0,0,1,0,0,0,0,0,0,0,2,0,0,0,0,1,1,0,0,0,0,0,3,0,0,0,0,0,0,1,1,0,
%T A331902 0,0,0,0,0,1,4,1,0,0,0,0,0,0,0,2,2,0,0,0,0,0,0,0,0,1,5,1,0,0,0,0,0,0,
%U A331902 0,0,1,1,1,1,0,0,0,0,0,0,0,0,0,1,6,1,0
%N A331902 T(n, k) = floor(n/m) where m is the least positive integer such that floor(n/m) = floor(k/m). Square array read by antidiagonals, for n >= 0 and k >= 0.
%C A331902 For any n > 0, the n-th row has A001651(n) nonzero terms.
%H A331902 Rémy Sigrist, <a href="/A331902/b331902.txt">Table of n, a(n) for n = 0..10010</a> (antidiagonals 0..140)
%H A331902 Rémy Sigrist, <a href="/A331886/a331886_1.png">Colored representation of T(n, k) for n, k = 0..1000</a> (where the hue is function of T(n, k), red pixels correspond to 0's)
%F A331902 T(n, k) = floor(n/A331886(n, k)) = floor(k/A331886(n, k)).
%F A331902 T(n, k) = T(k, n).
%F A331902 T(n, k) = 0 iff max(n, k) >= 2*min(n, k).
%F A331902 T(n, n+1) = A213633(n+1).
%e A331902 Array T(n, k) begins (with dots instead of 0's for readability):
%e A331902    n\k|   0   1   2   3   4   5   6   7   8   9  10  11  12
%e A331902    ---+----------------------------------------------------
%e A331902      0|   .   .   .   .   .   .   .   .   .   .   .   .   .
%e A331902      1|   .   1   .   .   .   .   .   .   .   .   .   .   .
%e A331902      2|   .   .   2   1   .   .   .   .   .   .   .   .   .
%e A331902      3|   .   .   1   3   1   1   .   .   .   .   .   .   .
%e A331902      4|   .   .   .   1   4   2   1   1   .   .   .   .   .
%e A331902      5|   .   .   .   1   2   5   1   1   1   1   .   .   .
%e A331902      6|   .   .   .   .   1   1   6   3   2   1   1   1   .
%e A331902      7|   .   .   .   .   1   1   3   7   2   1   1   1   1
%e A331902      8|   .   .   .   .   .   1   2   2   8   4   2   2   1
%e A331902      9|   .   .   .   .   .   1   1   1   4   9   3   3   1
%e A331902     10|   .   .   .   .   .   .   1   1   2   3  10   5   2
%e A331902     11|   .   .   .   .   .   .   1   1   2   3   5  11   2
%e A331902     12|   .   .   .   .   .   .   .   1   1   1   2   2  12
%o A331902 (PARI) T(n,k) = for (x=1, oo, if (n\x==k\x, return (n\x)))
%Y A331902 Cf. A001651, A213633, A331886.
%K A331902 nonn,tabl
%O A331902 0,13
%A A331902 _Rémy Sigrist_, Jan 31 2020