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A309455
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Number of squarefree parts in the partitions of n into 3 parts.
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1
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0, 0, 0, 3, 3, 6, 8, 11, 13, 18, 19, 24, 27, 33, 36, 44, 47, 54, 59, 66, 70, 81, 84, 95, 100, 111, 116, 128, 134, 146, 153, 165, 172, 186, 192, 207, 215, 230, 238, 256, 264, 281, 291, 309, 319, 340, 349, 369, 380, 400, 411, 432, 442, 464, 475, 497, 508, 532
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OFFSET
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0,4
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LINKS
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FORMULA
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a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} (mu(i)^2 + mu(j)^2 + mu(n-i-j)^2), where mu is the Möbius function (A008683).
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EXAMPLE
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Figure 1: The partitions of n into 3 parts for n = 3, 4, ...
1+1+8
1+1+7 1+2+7
1+2+6 1+3+6
1+1+6 1+3+5 1+4+5
1+1+5 1+2+5 1+4+4 2+2+6
1+1+4 1+2+4 1+3+4 2+2+5 2+3+5
1+1+3 1+2+3 1+3+3 2+2+4 2+3+4 2+4+4
1+1+1 1+1+2 1+2+2 2+2+2 2+2+3 2+3+3 3+3+3 3+3+4 ...
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n | 3 4 5 6 7 8 9 10 ...
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a(n) | 3 3 6 8 11 13 18 19 ...
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MATHEMATICA
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Table[Sum[Sum[MoebiusMu[i]^2 + MoebiusMu[j]^2 + MoebiusMu[n - i - j]^2, {i, j, Floor[(n - j)/2]}], {j, Floor[n/3]}], {n, 0, 50}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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