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A294233 Number of partitions of n into two parts with smaller part nonsquarefree and larger part squarefree. 1

%I

%S 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 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 8,8,10,1,9,9,10,3,8,10,9,4,8,11,11,3,9

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

%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(i)^2) * mu(n-i)^2, where mu is the Möbius function (A008683).

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

%Y Cf. A008683, A008966, A294232.

%K nonn,easy

%O 1,18

%A _Wesley Ivan Hurt_, Oct 25 2017

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Last modified September 21 21:32 EDT 2021. Contains 347605 sequences. (Running on oeis4.)