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A370896
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Partial alternating sums of the squarefree kernel function (A007947).
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1
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1, -1, 2, 0, 5, -1, 6, 4, 7, -3, 8, 2, 15, 1, 16, 14, 31, 25, 44, 34, 55, 33, 56, 50, 55, 29, 32, 18, 47, 17, 48, 46, 79, 45, 80, 74, 111, 73, 112, 102, 143, 101, 144, 122, 137, 91, 138, 132, 139, 129, 180, 154, 207, 201, 256, 242, 299, 241, 300, 270, 331, 269
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OFFSET
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1,3
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LINKS
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FORMULA
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a(n) = Sum_{k=1..n} (-1)^(k+1) * A007947(k).
a(n) = c * n^2 + O(R(n)), where c = A065463 / 10 = 0.07044422..., R(n) = x^(3/2)*exp(-c_1*log(n)^(3/5)/log(log(n))^(1/5)) unconditionally, or x^(7/5)*exp(c_2*log(n)/log(log(n))) assuming the Riemann hypothesis, and c_1 and c_2 are positive constants (Tóth, 2017).
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MATHEMATICA
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rad[n_] := Times @@ (First[#]& /@ FactorInteger[n]); Accumulate[Array[(-1)^(#+1) * rad[#] &, 100]]
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PROG
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(PARI) rad(n) = vecprod(factor(n)[, 1]);
lista(kmax) = {my(s = 0); for(k = 1, kmax, s += (-1)^(k+1) * rad(k); print1(s, ", "))};
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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