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A294232 Number of partitions of n into two parts with smaller part squarefree and larger part nonsquarefree. 1

%I

%S 0,0,0,0,1,1,1,0,1,2,2,1,2,3,3,1,2,2,3,1,3,3,4,1,3,4,4,3,5,6,6,3,5,5,

%T 6,1,5,6,6,2,5,6,5,2,5,8,8,3,6,8,9,3,7,7,10,4,7,7,9,4,8,9,9,5,9,10,10,

%U 4,10,10,12,2,10,10,11,5,11,13,12,6

%N Number of partitions of n into two parts with smaller part squarefree and larger part nonsquarefree.

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%F a(n) = Sum_{i=1..floor(n/2)} (1 - mu(n-i)^2) * mu(i)^2, where mu is the Möbius function (A008683).

%t Table[Sum[(1 - MoebiusMu[n - k]^2) (MoebiusMu[k]^2), {k, Floor[n/2]}], {n, 80}]

%Y Cf. A008683, A008966, A294233.

%K nonn,easy

%O 1,10

%A _Wesley Ivan Hurt_, Oct 25 2017

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Last modified October 15 15:39 EDT 2021. Contains 348033 sequences. (Running on oeis4.)