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 A375580 #34 Aug 23 2024 15:35:38 %S A375580 0,0,0,1,0,0,1,1,0,1,1,0,1,1,1,1,0,1,1,1,2,3,0,1,1,1,1,1,1,1,2,2,0,2, %T A375580 2,2,2,1,2,3,2,2,3,2,0,1,1,3,1,3,2,2,1,1,1,2,1,4,1,2,3,3,3,3,1,1,4,2, %U A375580 2,2,3,1,2,3,1,3,4,1,3,2,2,1,2,2,3,3,2,4 %N A375580 a(n) is the number of partitions n = x + y + z of positive integers such that x*y*z is a perfect cube. %C A375580 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 cube. %C A375580 Conjecture: for n > 176, a(n) > 0. - _Charles R Greathouse IV_, Aug 20 2024 %H A375580 Felix Huber and Charles R Greathouse IV, <a href="/A375580/b375580.txt">Table of n, a(n) for n = 0..10000</a> (up to 1000 from Huber) %H A375580 Felix Huber, <a href="/A375580/a375580_1.txt">Maple codes</a> %H A375580 David A. Corneth, <a href="/A375580/a375580.gp.txt">PARI program</a> %F A375580 Trivial upper bound: a(n) <= A069905(n). - _Charles R Greathouse IV_, Aug 23 2024 %e A375580 a(21) = 3 because the three partitions [1, 4, 16], [3, 6, 12], [7, 7, 7] satisfy the conditions: 1 + 4 + 16 = 21 and 1*4*16 = 4^3, 3 + 6 + 12 = 21 and 3*6*12 = 6^3, 7 + 7 + 7 = 21 and 7*7*7 = 7^3. %e A375580 See also linked Maple code. %p A375580 # See Huber link. %o A375580 (PARI) a(n)=sum(x=1,n\3, sum(y=x,(n-x)\2, ispower(x*y*(n-x-y),3))) \\ _Charles R Greathouse IV_, Aug 20 2024 %o A375580 (PARI) \\ See Corneth link %o A375580 (Python) %o A375580 from sympy import integer_nthroot %o A375580 def A375580(n): return sum(1 for x in range(n//3) for y in range(x,n-x-1>>1) if integer_nthroot((n-x-y-2)*(x+1)*(y+1),3)[1]) # _Chai Wah Wu_, Aug 21 2024 %Y A375580 Cf. A338939, A375512, A375576, A103277, A069905. %K A375580 nonn %O A375580 0,21 %A A375580 _Felix Huber_, Aug 19 2024