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A308840
Number of partitions of n into 5 squarefree parts.
9
0, 0, 0, 0, 0, 1, 1, 2, 2, 4, 5, 7, 7, 10, 11, 15, 15, 20, 22, 28, 29, 37, 39, 48, 49, 61, 63, 76, 77, 93, 97, 113, 115, 135, 140, 161, 164, 190, 196, 224, 228, 261, 269, 304, 308, 351, 360, 404, 412, 462, 475, 528, 538, 597, 612, 675, 685, 759, 774, 849
OFFSET
0,8
FORMULA
a(n) = Sum_{l=1..floor(n/5)} Sum_{k=l..floor((n-l)/4)} Sum_{j=k..floor((n-k-l)/3)} Sum_{i=j..floor((n-j-k-l)/2)} mu(l)^2 * mu(k)^2 * mu(j)^2 * mu(i)^2 * mu(n-i-j-k-l)^2, where mu is the Möbius function (A008683).
a(n) = A308839(n)/n.
EXAMPLE
The partitions of n into 5 parts for n = 10, 11, ..
1+1+1+1+10
1+1+1+2+9
1+1+1+3+8
1+1+1+4+7
1+1+1+5+6
1+1+1+1+9 1+1+2+2+8
1+1+1+2+8 1+1+2+3+7
1+1+1+3+7 1+1+2+4+6
1+1+1+4+6 1+1+2+5+5
1+1+1+5+5 1+1+3+3+6
1+1+1+1+8 1+1+2+2+7 1+1+3+4+5
1+1+1+2+7 1+1+2+3+6 1+1+4+4+4
1+1+1+3+6 1+1+2+4+5 1+2+2+2+7
1+1+1+1+7 1+1+1+4+5 1+1+3+3+5 1+2+2+3+6
1+1+1+2+6 1+1+2+2+6 1+1+3+4+4 1+2+2+4+5
1+1+1+3+5 1+1+2+3+5 1+2+2+2+6 1+2+3+3+5
1+1+1+1+6 1+1+1+4+4 1+1+2+4+4 1+2+2+3+5 1+2+3+4+4
1+1+1+2+5 1+1+2+2+5 1+1+3+3+4 1+2+2+4+4 1+3+3+3+4
1+1+1+3+4 1+1+2+3+4 1+2+2+2+5 1+2+3+3+4 2+2+2+2+6
1+1+2+2+4 1+1+3+3+3 1+2+2+3+4 1+3+3+3+3 2+2+2+3+5
1+1+2+3+3 1+2+2+2+4 1+2+3+3+3 2+2+2+2+5 2+2+2+4+4
1+2+2+2+3 1+2+2+3+3 2+2+2+2+4 2+2+2+3+4 2+2+3+3+4
2+2+2+2+2 2+2+2+2+3 2+2+2+3+3 2+2+3+3+3 2+3+3+3+3
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n | 10 11 12 13 14 ...
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a(n) | 5 7 7 10 11 ...
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- Wesley Ivan Hurt, Sep 16 2019
MATHEMATICA
Table[Sum[Sum[Sum[Sum[MoebiusMu[l]^2*MoebiusMu[k]^2*MoebiusMu[j]^2* MoebiusMu[i]^2*MoebiusMu[n - i - j - k - l]^2, {i, j, Floor[(n - j - k - l)/2]}], {j, k, Floor[(n - k - l)/3]}], {k, l, Floor[(n - l)/4]}], {l, Floor[n/5]}], {n, 0, 80}]
CROSSREFS
Sequence in context: A367962 A107849 A053036 * A067957 A120326 A036406
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jun 28 2019
STATUS
approved