This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A340805 #36 Oct 23 2022 09:20:17
%S A340805 1,1,1,2,2,3,2,3,2,3,2,4,2,4,3,4,2,5,2,4,3,4,2,6,2,4,4,5,2,6,2,5,4,4,
%T A340805 2,7,2,4,4,6,2,6,2,6,5,4,2,8,2,5,4,6,2,6,3,6,4,4,2,10,2,4,4,6,4,7,2,6,
%U A340805 4,6,2,9,2,4,6,6,2,7,2,8,4,4,2,10,4,4,4
%N A340805 a(n) is the number of solutions of the equation x*(y - 1) + (2*x - y - 1)*(x mod 2) = 2*n for 0 < x <= y.
%C A340805 Also the number of times 2*n+1 appears in A340804.
%C A340805 Offset is 1 because the equation x*(y - 1) + (2*x - y - 1)*(x mod 2) = 0 has an infinite number of positive integer solutions satisfying the inequality x <= y, or equivalently, A005408(0) = 1 appears infinitely many times in A340804.
%H A340805 Stefano Spezia, <a href="/A340805/b340805.txt">Table of n, a(n) for n = 1..10000</a>
%F A340805 a(n) = Sum_{d|n} ([d <= floor((1 + sqrt(1 + 8*n))/4)] + [d <= floor((sqrt(1 + 2*n) - 1)/2)]), where [ ] is the Iverson bracket.
%F A340805 A038548(n) <= a(n) <= A000005(n).
%F A340805 a(p) = A000005(p) = 2 if p is a prime greater than or equal to 5.
%e A340805 a(6) = 3 since there are 3 positive integer solutions (x, y) satisfying the inequality x <= y, i.e., (2, 4), (3, 5) and (4, 7).
%t A340805 Table[Sum[Boole[d<=Floor[(1+Sqrt[1+8n])/4]]+Boole[d<=Floor[(Sqrt[1+2n]-1)/2]],{d,Divisors[n]}],{n,87}]
%o A340805 (PARI) T(n, k) = 1 + k*(n - 1) + (2*k - n - 1)*(k % 2); \\ A340804
%o A340805 a(n) = sum(i=1, 2*n+1, sum(k=1, i, T(i, k) == 2*n+1)); \\ _Michel Marcus_, Jan 25 2021
%o A340805 (PARI) a(n) = sumdiv(n, d, (d <= (1 + sqrt(1 + 8*n))\4) + (d <= (sqrt(1 + 2*n) - 1)\2)); \\ _Michel Marcus_, Jan 25 2021
%Y A340805 Cf. A000005, A005408 (2*n+1), A038548, A340804.
%K A340805 nonn
%O A340805 1,4
%A A340805 _Stefano Spezia_, Jan 22 2021