OFFSET
1,2
COMMENTS
Row n has length n and columns are numbered k = 1..n.
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.
The end-most terms of the rows are A007952.
LINKS
Neal Gersh Tolunsky, Table of n, a(n) for n = 1..9870 (first 140 rows flattened)
FORMULA
EXAMPLE
Triangle begins:
n/k| 1 2 3 4 5 6 7
--------------------------------
1 | 1;
2 | 2, 3;
3 | 3, 4, 5;
4 | 4, 6, 8, 9;
5 | 5, 8, 9, 10, 11;
6 | 6, 10, 12, 15, 16, 17;
7 | 7, 12, 15, 16, 18, 20, 21;
...
For row n=6, the numbers of the chain, and below them their divisors are:
6 10 12 15 16 17
6 5 4 3 2 1
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Tamas Sandor Nagy, Sep 28 2022
STATUS
approved