A263730 Irregular triangle read by rows in which row n > 1 lists k such that (k^2 + k*n)/(k + 1) is an integer.

0, 0, 1, 0, 2, 0, 1, 3, 0, 4, 0, 1, 2, 5, 0, 6, 0, 1, 3, 7, 0, 2, 8, 0, 1, 4, 9, 0, 10, 0, 1, 2, 3, 5, 11, 0, 12, 0, 1, 6, 13, 0, 2, 4, 14, 0, 1, 3, 7, 15, 0, 16, 0, 1, 2, 5, 8, 17, 0, 18, 0, 1, 3, 4, 9, 19, 0, 2, 6, 20, 0, 1, 10, 21, 0, 22, 0, 1, 2, 3, 5, 7, 11, 23, 0, 4, 24, 0, 1, 12, 25

Offset: 2

Author

Juri-Stepan Gerasimov, Oct 25 2015

Keywords

• nonn
• tabf

Comments

Minimal value of k is 0 and maximal value of k is n - 2 for n-th row.

Length of rows gives A000005.

Sum of rows gives A065608.

Examples

			  n\k| 0   1   2   3   4   5   6   7   8   9  10
  ---+------------------------------------------
   0 | 0
   1 | 0   1   2   3   4   5   6   7   8   9  10
   2 | 0
   3 | 0   1
   4 | 0   2
   5 | 0   1   3
   6 | 0   4
   7 | 0   1   2   5
   8 | 0   6
   9 | 0   1   3   7
  10 | 0   2   8
  11 | 0   1   4   9
  12 | 0  10
  13 | 0   1   2   3   5  11
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 2..1000

Crossrefs

Cf. A000005, A065608, A027750, A263729.

Programs

Mathematica

Table[Select[Range[0,n-2],Divisible[#^2+n #,#+1]&],{n,30}]//Flatten (* Harvey P. Dale, Dec 27 2016 *)

PARI

tabf(nn) = {for (n=2, nn, for (k=0, n, if (!((k^2 + k*n) % (k+1)), print1(k, ", "));); print(););} \\ Michel Marcus, Oct 25 2015

Formula

a(n) = A027750(n) - 1.