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 A294233 #13 Jul 16 2025 09:22:55
%S A294233 0,0,0,0,0,0,0,0,1,1,1,0,0,1,1,0,1,2,3,1,2,2,3,1,3,3,3,1,2,3,3,1,3,3,
%T A294233 4,0,4,5,5,2,5,6,5,2,4,6,6,2,5,7,8,2,5,6,9,4,7,7,9,4,7,8,8,4,8,9,9,3,
%U A294233 8,8,10,1,9,9,10,3,8,10,9,4,8,11,11,3,9
%N A294233 Number of partitions of n into two parts with smaller part nonsquarefree and larger part squarefree.
%H A294233 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A294233 a(n) = Sum_{i=1..floor(n/2)} mu(n-i)^2 * (1 - mu(i)^2), where mu is the Möbius function (A008683).
%F A294233 a(n) = A294101(n) - A294232(n). - _Wesley Ivan Hurt_, Jul 16 2025
%t A294233 Table[Sum[(1 - MoebiusMu[k]^2) MoebiusMu[n - k]^2, {k, Floor[n/2]}], {n, 80}]
%Y A294233 Cf. A008683, A008966, A294101, A294232.
%K A294233 nonn,easy
%O A294233 1,18
%A A294233 _Wesley Ivan Hurt_, Oct 25 2017