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Number of partitions of n into exactly two parts, at least one of which is squarefree.
1

%I #5 Feb 21 2022 10:46:56

%S 0,1,1,2,2,3,3,3,4,5,5,5,5,7,7,6,7,8,9,8,9,10,11,9,11,12,12,11,12,14,

%T 14,12,14,15,16,12,16,18,18,15,18,20,19,17,19,22,22,18,21,23,24,19,22,

%U 23,26,21,24,25,27,23,26,28,28,24,28,30,30,25,30,31,33,24,32,33,34,28

%N Number of partitions of n into exactly two parts, at least one of which is squarefree.

%F a(n) = Sum_{k=1..floor(n/2)} (mu(k)^2 + mu(n-k)^2 - mu(k)^2*mu(n-k)^2), where mu is the Möbius function.

%Y Cf. A005117, A008683 (mu), A351834 (two distinct parts).

%K nonn

%O 1,4

%A _Wesley Ivan Hurt_, Feb 21 2022