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%I #10 Dec 13 2021 17:06:10
%S 2,2,3,2,3,4,4,2,3,4,5,4,2,3,4,5,6,4,6,6,2,3,4,5,6,7,4,6,6,2,3,4,5,6,
%T 7,8,4,6,8,6,8,2,3,4,5,6,7,8,9,4,6,8,6,9,8,2,3,4,5,6,7,8,9,10,4,6,8,
%U 10,6,9,8,10,2,3,4,5,6,7,8,9,10,11,4,6,8,10,6,9,8,10,2,3,4,5,6,7,8,9,10,11,12,4,6,8,10,12,6,9,12,8,12,10,12
%N Irregular triangle read by rows: row n gives for n >= 2 a concatenation of the finite sequences of the multiples of k, larger than k and not exceeding n, for k = 1, 2, ..., floor(n/2).
%C The length of row n is A002541(n).
%C The sum of row n is A348392(n).
%C The lengths of the sublists for these multiples of k in row n are given by T(n, k) = A348388(n, k), for n >= 2 and k = 1, 2, ..., floor(n/2).
%F The entries a(n, m) of row n, for n > = 2 and m = 1, 2, ..., A002541(n), are given by the concatenation of the sequences k*(2, 3, ..., t(n,k)) for k = 1, 2, ..., floor(n/2), with t(n, k) = floor((n-k)/k) + 1.
%e The irregular triangle a(n, m) begins: (the k-sublists are separated by a vertical bar)
%e n\m 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 ...
%e -------------------------------------------------------------------------
%e 2: 2
%e 3: 2 3
%e 4: 2 3 4|4
%e 5: 2 3 4 5|4
%e 6: 2 3 4 5 6|4 6|6
%e 7: 2 3 4 5 6 7|4 6| 6
%e 8: 2 3 4 5 6 7 8|4 6 8| 6| 8
%e 9: 2 3 4 5 6 7 8 9| 4 6 8| 6 9| 8
%e 10: 2 3 4 5 6 7 8 9 10| 4 6 8 10| 6 9| 8|10
%e 11: 2 3 4 5 6 7 8 9 10 11| 4 6 8 10| 6 9| 8|10
%e 12: 2 3 4 5 6 7 8 9 10 11 12| 4 6 8 10 12| 6 9 12| 8 12|10|12
%e 13: 2 3 4 5 6 7 8 9 10 11 12 13| 4 6 8 10 12| 6 9 12| 8 12|10|12
%e ...
%t nrows=10;Table[Flatten[Table[Range[2k,n,k],{k,Floor[n/2]}]],{n,2,nrows+1}] (* _Paolo Xausa_, Nov 23 2021 *)
%Y Cf. A002541, A348388, A348392.
%K nonn,easy,tabf
%O 2,1
%A _Wolfdieter Lang_, Oct 31 2021
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