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 A375576 #20 Aug 28 2024 11:18:28 %S A375576 0,0,0,1,0,1,1,1,1,1,1,4,1,2,3,2,2,4,2,4,3,4,2,5,4,2,6,5,2,8,4,8,4,4, %T A375576 5,10,5,3,8,7,6,12,5,6,7,6,7,11,5,6,8,12,6,11,8,11,11,6,3,22,6,12,12, %U A375576 8,9,13,12,7,14,14,6,18,7,7,18,13,14,13,7,19,10 %N A375576 a(n) is the number of partitions n = x + y + z of positive integers such that x*y*z is a perfect square. %C A375576 a(n) is also the number of distinct integer-sided cuboids with total edge length 4*n whose unit cubes can be grouped to a square cuboid with height 1. %H A375576 Felix Huber, <a href="/A375576/b375576.txt">Table of n, a(n) for n = 0..1000</a> %H A375576 Felix Huber, <a href="/A375576/a375576_1.txt">Maple Codes</a> %e A375576 a(24) = 4 because the four partitions [2, 4, 18], [3, 9, 12], [4, 4, 16], [4, 10, 10] satisfy the conditions: 2 + 4 + 18 = 24 and 2*4*18 = 12^2, 3 + 9 + 12 = 24 and 3*9*12 = 18^2, 4 + 4 + 16 = 24 and 4*4*16 = 16^2, 4 + 10 + 10 = 24 and 4*10*10 = 20^2. %e A375576 See also linked Maple code. %p A375576 See Huber link. %o A375576 (Python) %o A375576 from sympy.ntheory.primetest import is_square %o A375576 def A375567(n): return sum(1 for x in range(n//3) for y in range(x,n-x-1>>1) if is_square((n-x-y-2)*(x+1)*(y+1))) # _Chai Wah Wu_, Aug 22 2024 %Y A375576 Cf. A338939, A375512, A375580. %K A375576 nonn %O A375576 0,12 %A A375576 _Felix Huber_, Aug 19 2024