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A262871
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Sum of the squarefree numbers appearing among the smaller parts of the partitions of n into two parts.
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7
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0, 1, 1, 3, 3, 6, 6, 6, 6, 11, 11, 17, 17, 24, 24, 24, 24, 24, 24, 34, 34, 45, 45, 45, 45, 58, 58, 72, 72, 87, 87, 87, 87, 104, 104, 104, 104, 123, 123, 123, 123, 144, 144, 166, 166, 189, 189, 189, 189, 189, 189, 215, 215, 215, 215, 215, 215, 244, 244, 274
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OFFSET
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1,4
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LINKS
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FORMULA
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a(n) = Sum_{i=1..floor(n/2)} i * mu(i)^2, where mu is the Möebius function (A008683).
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EXAMPLE
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a(5)=3; there are two partitions of 5 into two parts: (4,1) and (3,2). The sum of the smaller squarefree parts is 1+2=3. Thus a(5)=3.
a(6)=6; there are three partitions of 6 into two parts: (5,1), (4,2) and (3,3). All of the smaller parts are squarefree, so a(6) = 1+2+3 = 6.
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MAPLE
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with(numtheory): A262871:=n->add(i*mobius(i)^2, i=1..floor(n/2)): seq(A262871(n), n=1..100);
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MATHEMATICA
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Table[Sum[i*MoebiusMu[i]^2, {i, Floor[n/2]}], {n, 70}]
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PROG
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(PARI) a(n) = sum(i=1, n\2, i * moebius(i)^2); \\ Michel Marcus, Oct 04 2015
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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