A341829 - OEIS

%I #14 Oct 23 2022 09:20:12

%S 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,

%T 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,

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

%N 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.

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

%H Stefano Spezia, <a href="/A341829/b341829.txt">Table of n, a(n) for n = 1..10175</a> (first 1500 rows of the triangle, flattened).

%e Triangle begins:

%e 2

%e 2

%e 2

%e 2   3

%e 2   3

%e 2   3   4

%e 2   3

%e 2   3   4

%e 2   3

%e 2   3   4

%e 2   3

%e 2   3   4   5

%e 2   3

%e 2   3   4   5

%e 2   3   6

%e 2   3   4   5

%e 2   3

%e 2   3   4   5   6

%e ...

%t 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

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

%K nonn,tabf

%O 1,1

%A _Stefano Spezia_, Feb 21 2021