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 A359944 #24 Aug 18 2024 20:48:58
%S A359944 1,2,1,2,1,2,1,2,2,2,1,2,1,2,1,2,1,3,1,2,1,2,1,2,1,2,2,3,1,2,1,2,1,2,
%T A359944 1,3,1,2,1,2,1,2,1,2,2,2,1,2,1,2,1,2,1,3,1,3,1,2,1,2,1,2,2,2,2,2,1,2,
%U A359944 1,2,1,3,1,2,1,2,1,2,1,2,2,2,1,3,1,2,1,2,1,3,1
%N A359944 Number of divisors d of n such that d-1 is a cube.
%C A359944 The Cartesian equation for the Folium of Descartes is given as x^3 + y^3 = 3*k*x*y. If we set 3*k = n, then a(n)-1 is the number of integer solutions such that x,y > 0 and y >= x. Let d = m^3+1 be a divisor of n, then x = 3*k*m/(m^3+1); y = 3*k*m^2/(m^3+1) is a solution. - _Thomas Scheuerle_, Aug 07 2024
%F A359944 G.f.: Sum_{k>=0} x^(k^3+1)/(1 - x^(k^3+1)).
%F A359944 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{k>=0} 1/(k^3+1) = 1 + A339606 = 1.686503... . - _Amiram Eldar_, Jan 01 2024
%t A359944 a[n_] := DivisorSum[n, 1 &, IntegerQ[Surd[#-1, 3]] &]; Array[a, 100] (* _Amiram Eldar_, Aug 09 2023 *)
%o A359944 (PARI) a(n) = sumdiv(n, d, ispower(d-1, 3));
%Y A359944 Cf. A001093, A061704, A339606.
%K A359944 nonn
%O A359944 1,2
%A A359944 _Seiichi Manyama_, Jan 19 2023