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

0, 1, 2, 7, 6, 22, 22, 38, 52, 70, 58, 141, 104, 188, 230, 281, 260, 320, 374, 531, 526, 717, 566, 927, 756, 1017, 1114, 1203, 1148, 1799, 1402, 1741, 1718, 2170, 2314, 2765, 2400, 2912, 2800, 3769, 2856, 4577, 3352, 4923, 4410, 5054, 5036, 6346, 6246, 5537

Offset: 1

Author

Adnan Baysal, Mar 28 2024

Keywords

• nonn

Comments

Construct the same directed graph as in A369793. a(n) is the sum of vertices directed to the vertex n in this graph.

Examples

			a(1) = 0 since 1 does not exist in A063655.
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.
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.
		

Crossrefs

Cf. A056737, A063655, A369110, A369793.

Programs

Python

from sympy import divisors
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)