A341829 Irregular triangle read by rows: the n-th row gives the x-values of the solutions of the equation x*(y - 1) + (2*x - y - 1)*(x mod 2) = 2*n for 0 < x <= y.

2, 2, 2, 2, 3, 2, 3, 2, 3, 4, 2, 3, 2, 3, 4, 2, 3, 2, 3, 4, 2, 3, 2, 3, 4, 5, 2, 3, 2, 3, 4, 5, 2, 3, 6, 2, 3, 4, 5, 2, 3, 2, 3, 4, 5, 6, 2, 3, 2, 3, 4, 5, 2, 3, 6, 2, 3, 4, 5, 2, 3, 2, 3, 4, 5, 6, 7, 2, 3, 2, 3, 4, 5, 2, 3, 6, 7, 2, 3, 4, 5, 8, 2, 3, 2, 3, 4, 5, 6, 7

Offset: 1

Author

Stefano Spezia, Feb 21 2021

Keywords

• nonn
• tabf

Comments

Equivalently, the n-th row gives the column indices corresponding to 2*n + 1 in the triangle A340804.

Examples

			Triangle begins:
2
2
2
2   3
2   3
2   3   4
2   3
2   3   4
2   3
2   3   4
2   3
2   3   4   5
2   3
2   3   4   5
2   3   6
2   3   4   5
2   3
2   3   4   5   6
...
		

Links

• Stefano Spezia, Table of n, a(n) for n = 1..10175 (first 1500 rows of the triangle, flattened).

Crossrefs

Cf. A005843, A340804, A340805 (row length or solutions number), A341830 (y-values).

Programs

Mathematica

Table[Union[2Intersection[Divisors[n],Table[d,{d,Floor[(1+Sqrt[1+8n])/4]}]],2Intersection[Divisors[n],Table[d,{d,Floor[(Sqrt[1+2n]-1)/2]}]]+1],{n,30}]//Flatten