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 A286971 #6 Feb 24 2021 09:09:13
%S A286971 0,0,0,1,1,0,1,0,2,1,0,1,2,2,1,1,1,4,2,2,2,2,1,3,3,3,2,3,3,4,1,3,3,4,
%T A286971 2,3,3,5,5,4,5,5,3,5,6,6,4,3,4,4,3,7,7,6,3,3,6,8,6,4,4,3,8,8,8,7,2,7,
%U A286971 10,8,5,5,6,4,8,8,12,7,3,7,11,11,8,3,7,9,6,10,14,8,4,5,12,13,10,7,9,8,12,13,12
%N A286971 Number of ways to write n as a sum of two numbers, one of which is the product of an even number of distinct primes (including 1) (A030229) and another is the product of an odd number of distinct primes (A030059).
%C A286971 Conjecture: a(n) > 0 for all n > 10.
%F A286971 G.f.: (Sum_{i>=1} x^A030229(i))*(Sum_{j>=1} x^A030059(j)).
%e A286971 a(17) = 4 because we have [15, 2], [14, 3], [11, 6] and [10, 7].
%t A286971 nmax = 100; CoefficientList[Series[(Sum[Boole[MoebiusMu[k] == 1] x^k, {k, 1, nmax}]) (Sum[Boole[MoebiusMu[k] == -1] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]
%Y A286971 Cf. A005117, A030059, A030229, A098235, A098236, A285796, A285797.
%K A286971 nonn
%O A286971 0,9
%A A286971 _Ilya Gutkovskiy_, May 17 2017