A263730 - OEIS

%I #23 Dec 27 2016 19:09:35

%S 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,

%T 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,

%U 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

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

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

%C Length of rows gives A000005.

%C Sum of rows gives A065608.

%H Harvey P. Dale, <a href="/A263730/b263730.txt">Table of n, a(n) for n = 2..1000</a>

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

%e   n\k| 0   1   2   3   4   5   6   7   8   9  10

%e   ---+------------------------------------------

%e    0 | 0

%e    1 | 0   1   2   3   4   5   6   7   8   9  10

%e    2 | 0

%e    3 | 0   1

%e    4 | 0   2

%e    5 | 0   1   3

%e    6 | 0   4

%e    7 | 0   1   2   5

%e    8 | 0   6

%e    9 | 0   1   3   7

%e   10 | 0   2   8

%e   11 | 0   1   4   9

%e   12 | 0  10

%e   13 | 0   1   2   3   5  11

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

%o (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

%Y Cf. A000005, A065608, A027750, A263729.

%K nonn,tabf

%O 2,5

%A _Juri-Stepan Gerasimov_, Oct 25 2015