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A348389 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).

%I A348389 #10 Dec 13 2021 17:06:10
%S A348389 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 A348389 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 A348389 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 A348389 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 A348389 The length of row n is A002541(n).
%C A348389 The sum of row n is A348392(n).
%C A348389 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 A348389 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 A348389 The irregular triangle a(n, m) begins: (the k-sublists are separated by a vertical bar)
%e A348389 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 A348389 -------------------------------------------------------------------------
%e A348389 2:    2
%e A348389 3:    2 3
%e A348389 4:    2 3 4|4
%e A348389 5:    2 3 4 5|4
%e A348389 6:    2 3 4 5 6|4 6|6
%e A348389 7:    2 3 4 5 6 7|4 6| 6
%e A348389 8:    2 3 4 5 6 7 8|4  6  8| 6| 8
%e A348389 9:    2 3 4 5 6 7 8 9| 4  6  8| 6  9| 8
%e A348389 10:   2 3 4 5 6 7 8 9 10| 4  6  8 10| 6  9| 8|10
%e A348389 11:   2 3 4 5 6 7 8 9 10 11| 4  6  8 10| 6  9| 8|10
%e A348389 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 A348389 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 A348389 ...
%t A348389 nrows=10;Table[Flatten[Table[Range[2k,n,k],{k,Floor[n/2]}]],{n,2,nrows+1}] (* _Paolo Xausa_, Nov 23 2021 *)
%Y A348389 Cf. A002541, A348388, A348392.
%K A348389 nonn,easy,tabf
%O A348389 2,1
%A A348389 _Wolfdieter Lang_, Oct 31 2021