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A371597 a(n) is the sum of k where A063655(k) = n.

%I A371597 #7 Apr 24 2024 13:22:22
%S A371597 0,1,2,7,6,22,22,38,52,70,58,141,104,188,230,281,260,320,374,531,526,
%T A371597 717,566,927,756,1017,1114,1203,1148,1799,1402,1741,1718,2170,2314,
%U A371597 2765,2400,2912,2800,3769,2856,4577,3352,4923,4410,5054,5036,6346,6246,5537
%N A371597 a(n) is the sum of k where A063655(k) = n.
%C A371597 Construct the same directed graph as in A369793. a(n) is the sum of vertices directed to the vertex n in this graph.
%e A371597 a(1) = 0 since 1 does not exist in A063655.
%e A371597 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 at index 1, which means a(2) = 1.
%e A371597 a(4) = 7, 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.
%o A371597 (Python)
%o A371597 from sympy import divisors
%o A371597 def A371597(n): return sum(m for m in range(1, (n**2>>2)+1) if (d:=divisors(m))[((l:=len(d))-1)>>1]+d[l>>1]==n)
%Y A371597 Cf. A056737, A063655, A369110, A369793.
%K A371597 nonn
%O A371597 1,3
%A A371597 _Adnan Baysal_, Mar 28 2024