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 A369793 #36 Mar 25 2024 06:48:57
%S A369793 0,1,1,2,1,3,2,3,3,3,2,5,3,5,5,5,4,5,5,7,6,7,5,8,6,7,7,7,6,10,7,9,8,9,
%T A369793 9,10,8,10,9,11,8,13,9,13,11,12,11,14,13,11,12,15,10,15,13,15,13,14,
%U A369793 12,15,12,18,16,15,15,17,13,17
%N A369793 a(n) is the number of occurrences of n in A063655.
%C A369793 Construct a directed graph whose vertex set is the set of all positive integers, and a directed edge from k to n belongs to this graph iff A063655(k) = n. a(n) is the in-degree of the vertex n in this graph. As conjectured in A369110, it is also conjectured here that the only cycles in this graph are from 4 to itself and between 5 and 6.
%e A369793 a(1) = 0 since 1 does not exist in A063655. This is also clear from the definition of A063655, because there is no integral rectangle with semiperimeter 1.
%e A369793 a(2) = 1 because there is only one integral rectangle of area 1 with a minimal semiperimeter 2, which is the 1 X 1 square. So 2 appears only once in A063655, which means a(2) = 1.
%e A369793 a(4) = 2, because only A063655(3) and A063655(4) have the value 4. For any n > 4, A063655(n) > 4, because A063655(n) > 2 * sqrt(n) > 2 * sqrt(4) = 4. Hence, 4 cannot appear in the rest of A063655.
%t A369793 a=1156;Table[Count[Table[2*Median[Divisors[m]], {m,a}] ,n],{n,Floor[2*Sqrt[a]]}] (* _James C. McMahon_, Mar 12 2024 *)
%o A369793 (Python)
%o A369793 from sympy import divisors
%o A369793 def A369793(n): return sum(1 for m in range(1,(n**2>>2)+1) if (d:=divisors(m))[((l:=len(d))-1)>>1]+d[l>>1]==n) # _Chai Wah Wu_, Mar 25 2024
%Y A369793 Cf. A063655, A369110, A056737.
%K A369793 nonn
%O A369793 1,4
%A A369793 _Adnan Baysal_, Feb 07 2024