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A357817
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Partial alternating sums of the Dedekind psi function (A001615): a(n) = Sum_{k=1..n} (-1)^(k+1) * psi(k).
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10
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1, -2, 2, -4, 2, -10, -2, -14, -2, -20, -8, -32, -18, -42, -18, -42, -24, -60, -40, -76, -44, -80, -56, -104, -74, -116, -80, -128, -98, -170, -138, -186, -138, -192, -144, -216, -178, -238, -182, -254, -212, -308, -264, -336, -264, -336, -288, -384, -328, -418
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = -(3/(2*Pi^3)) * n^2 + O(n * log(n)^(2/3)) (Tóth, 2017).
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MATHEMATICA
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psi[n_] := n * Times @@ (1 + 1/Transpose[FactorInteger[n]][[1]]); psi[1] = 1; Accumulate[Array[(-1)^(# + 1)*psi[#] &, 50]]
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PROG
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(PARI) f(n) = n * sumdivmult(n, d, issquarefree(d)/d); \\ A001615
a(n) = sum(k=1, n, (-1)^(k+1) * f(k)); \\ Michel Marcus, Oct 15 2022
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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