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A075993 Triangle read by rows: T(n,m) is the number of integers k such that floor(n/k) = m, n >= 1, k = 1..n.

%I A075993 #22 Jun 18 2025 23:16:45
%S A075993 1,1,1,2,0,1,2,1,0,1,3,1,0,0,1,3,1,1,0,0,1,4,1,1,0,0,0,1,4,2,0,1,0,0,
%T A075993 0,1,5,1,1,1,0,0,0,0,1,5,2,1,0,1,0,0,0,0,1,6,2,1,0,1,0,0,0,0,0,1,6,2,
%U A075993 1,1,0,1,0,0,0,0,0,1,7,2,1,1,0,1,0,0,0,0,0,0,1,7,3,1,1,0,0,1,0,0,0,0,0,0,1
%N A075993 Triangle read by rows: T(n,m) is the number of integers k such that floor(n/k) = m, n >= 1, k = 1..n.
%C A075993 The sum of numbers in row n is n.
%C A075993 Number of terms > 0 per row: Sum_{k=1..n} A057427(T(n,k)) = A055086(n). - _Reinhard Zumkeller_, Apr 06 2006
%H A075993 Michael De Vlieger, <a href="/A075993/b075993.txt">Table of n, a(n) for n = 1..11325</a> (rows 1 <= n <= 150, flattened)
%F A075993 T(n, m) = floor(n/m) - floor(n/(m+1)).
%e A075993 T(5, 1) = 3 counts k such that floor(5/k) = 1, namely k = 5, 4, 3.
%e A075993 First 10 rows:
%e A075993   1
%e A075993   1 1
%e A075993   2 0 1
%e A075993   2 1 0 1
%e A075993   3 1 0 0 1
%e A075993   3 1 1 0 0 1
%e A075993   4 1 1 0 0 0 1
%e A075993   4 2 0 1 0 0 0 1
%e A075993   5 1 1 1 0 0 0 0 1
%e A075993   5 2 1 0 1 0 0 0 0 1
%t A075993 Table[Floor[n/m] - Floor[n/(m + 1)], {n, 14}, {m, n}] // Flatten (* _Michael De Vlieger_, Jan 14 2022 *)
%Y A075993 Columns 1, 2, 3 are essentially A004526, A008615, A008679.
%Y A075993 Cf. A010766.
%K A075993 nonn,tabl
%O A075993 1,4
%A A075993 _Clark Kimberling_, Sep 28 2002