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A341830 Irregular triangle read by rows: the n-th row gives the y-values of the solutions of the equation x*(y - 1) + (2*x - y - 1)*(x mod 2) = 2*n for 0 < x <= y.

%I A341830 #14 Oct 23 2022 09:20:07
%S A341830 2,3,4,3,5,4,6,4,5,7,6,8,5,7,9,8,10,6,9,11,10,12,5,7,11,13,12,14,6,8,
%T A341830 13,15,6,14,16,7,9,15,17,16,18,7,8,10,17,19,18,20,9,11,19,21,8,20,22,
%U A341830 10,12,21,23,22,24,7,9,11,13,23,25,24,26,12,14,25,27,8,10,26,28
%N A341830 Irregular triangle read by rows: the n-th row gives the y-values of the solutions of the equation x*(y - 1) + (2*x - y - 1)*(x mod 2) = 2*n for 0 < x <= y.
%C A341830 Equivalently, the n-th row gives the row indices corresponding to 2*n + 1 in the triangle A340804.
%H A341830 Stefano Spezia, <a href="/A341830/b341830.txt">Table of n, a(n) for n = 1..10175</a> (first 1500 rows of the triangle, flattened).
%e A341830 Triangle begins:
%e A341830    2
%e A341830    3
%e A341830    4
%e A341830    3   5
%e A341830    4   6
%e A341830    4   5   7
%e A341830    6   8
%e A341830    5   7   9
%e A341830    8  10
%e A341830    6   9  11
%e A341830   10  12
%e A341830    5   7  11  13
%e A341830   12  14
%e A341830    6   8  13  15
%e A341830    6  14  16
%e A341830    7   9  15  17
%e A341830   16  18
%e A341830    7   8  10  17  19
%e A341830   ...
%t A341830 Table[Union[n/Intersection[Divisors[n],Table[d,{d,Floor[(1+Sqrt[1+8n])/4]}]]+1,n/Intersection[Divisors[n],Table[d,{d,Floor[(Sqrt[1+2n]-1)/2]}]]-1],{n,27}]//Flatten
%Y A341830 Cf. A005843, A340804, A340805 (row length or solutions number), A341829 (x-values).
%K A341830 nonn,tabf
%O A341830 1,1
%A A341830 _Stefano Spezia_, Feb 21 2021