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

2,5

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.

Links

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

Formula

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

Example

  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

Mathematica

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

Prog

(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

Crossrefs

Cf. A000005, A065608, A027750, A263729.

Sequence in context: A296046 A060318 A246061 * A331533 A089994 A178107

Adjacent sequences: A263727 A263728 A263729 * A263731 A263732 A263733

Keyword

nonn,tabf

Author

Juri-Stepan Gerasimov, Oct 25 2015

Status

approved