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A236532 Triangle T(n,k) read by rows: T(n,k) = floor(n*k/(n+k)), with 1 <= k <= n.

%I A236532 #23 Aug 07 2025 14:48:10
%S A236532 0,0,1,0,1,1,0,1,1,2,0,1,1,2,2,0,1,2,2,2,3,0,1,2,2,2,3,3,0,1,2,2,3,3,
%T A236532 3,4,0,1,2,2,3,3,3,4,4,0,1,2,2,3,3,4,4,4,5,0,1,2,2,3,3,4,4,4,5,5,0,1,
%U A236532 2,3,3,4,4,4,5,5,5,6,0,1,2,3,3,4,4,4,5,5
%N A236532 Triangle T(n,k) read by rows: T(n,k) = floor(n*k/(n+k)), with 1 <= k <= n.
%C A236532 It appears that the least m such that T(m, n) = n-1 is given by A103505(n) for n>= 1. - _Michel Marcus_, Feb 25 2020
%H A236532 Andrew Howroyd, <a href="/A236532/b236532.txt">Table of n, a(n) for n = 1..1275</a> (first 50 rows)
%F A236532 T(n, n) = floor(n/2). See A004526. - _Michel Marcus_, Feb 25 2020
%e A236532 Triangle begins:
%e A236532   0
%e A236532   0 1
%e A236532   0 1 1
%e A236532   0 1 1 2
%e A236532   0 1 1 2 2
%e A236532   0 1 2 2 2 3
%e A236532   0 1 2 2 2 3 3
%e A236532   0 1 2 2 3 3 3 4
%e A236532   0 1 2 2 3 3 3 4 4
%e A236532   0 1 2 2 3 3 4 4 4 5
%e A236532   0 1 2 2 3 3 4 4 4 5 5
%e A236532   0 1 2 3 3 4 4 4 5 5 5 6
%e A236532   0 1 2 3 3 4 4 4 5 5 5 6 6
%e A236532   0 1 2 3 3 4 4 5 5 5 6 6 6 7
%e A236532   0 1 2 3 3 4 4 5 5 6 6 6 6 7 7
%e A236532   0 1 2 3 3 4 4 5 5 6 6 6 7 7 7 8
%e A236532   0 1 2 3 3 4 4 5 5 6 6 7 7 7 7 8 8
%e A236532   0 1 2 3 3 4 5 5 6 6 6 7 7 7 8 8 8 9
%o A236532 (Python)
%o A236532 for n in range(1, 21):
%o A236532   for k in range(1, n+1):
%o A236532     print(n*k // (n+k), end=', ')
%o A236532   #print() # Uncomment to display as a triangle
%o A236532 (PARI) T(n,k)={n*k\(n+k)} \\ _Andrew Howroyd_, Feb 24 2020
%Y A236532 Cf. A004526, A103505.
%K A236532 nonn,easy,tabl
%O A236532 1,10
%A A236532 _Alex Ratushnyak_, Jan 27 2014