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A357431 Triangle read by rows where each term in row n is the next greater multiple of n..1.

%I A357431 #39 May 10 2023 06:25:08
%S A357431 1,2,3,3,4,5,4,6,8,9,5,8,9,10,11,6,10,12,15,16,17,7,12,15,16,18,20,21,
%T A357431 8,14,18,20,24,27,28,29,9,16,21,24,25,28,30,32,33,10,18,24,28,30,35,
%U A357431 36,39,40,41,11,20,27,32,35,36,40,44,45,46,47
%N A357431 Triangle read by rows where each term in row n is the next greater multiple of n..1.
%C A357431 Row n has length n and columns are numbered k = 1..n.
%C A357431 Row n begins with n which is trivially divisible by n. This is followed by the least number greater than n that is divisible by n-1. Next comes the least number that is greater than this preceding one and is divisible by n-2. Then it continues the same way until the last one is reached, which is trivially divisible by 1.
%C A357431 The end-most terms of the rows are A007952.
%H A357431 Neal Gersh Tolunsky, <a href="/A357431/b357431.txt">Table of n, a(n) for n = 1..9870</a> (first 140 rows flattened)
%F A357431 T(n,1) = n.
%F A357431 T(n,k) = T(n,k-1) + (n-k+1) - (T(n,k-1) mod (n-k+1)), for k >= 2.
%F A357431 T(n,n) = A007952(n).
%e A357431 Triangle begins:
%e A357431   n/k|  1   2   3   4   5   6   7
%e A357431   --------------------------------
%e A357431   1  |  1;
%e A357431   2  |  2,  3;
%e A357431   3  |  3,  4,  5;
%e A357431   4  |  4,  6,  8,  9;
%e A357431   5  |  5,  8,  9, 10, 11;
%e A357431   6  |  6, 10, 12, 15, 16, 17;
%e A357431   7  |  7, 12, 15, 16, 18, 20, 21;
%e A357431   ...
%e A357431 For row n=6, the numbers of the chain, and below them their divisors are:
%e A357431   6 10 12 15 16 17
%e A357431   6  5  4  3  2  1
%t A357431 row[n_] := Module[{k = n, s = Table[0, n], r}, s[[1]] = n;Do[k++; k += If[(r = Mod[k, i]) == 0, 0, i - Mod[k, i]]; s[[n+1-i]] = k, {i, n - 1, 1, -1}]; s]; Array[row, 11] // Flatten (* _Amiram Eldar_, Sep 28 2022 *)
%o A357431 (PARI) row(n) = my(v=vector(n)); v[1] = n; for (k=2, n, v[k] = v[k-1] + (n-k+1) - (v[k-1] % (n-k+1));); v; \\ _Michel Marcus_, Nov 16 2022
%Y A357431 Cf. A357417 (row sums), A357498, A007952 (right diagonal).
%K A357431 nonn,tabl
%O A357431 1,2
%A A357431 _Tamas Sandor Nagy_, Sep 28 2022