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A349621
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Dirichlet convolution of A003415 with the Dirichlet inverse of A003959.
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5
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0, 1, 1, 1, 1, -2, 1, 0, 2, -2, 1, -3, 1, -2, -2, -4, 1, -5, 1, -3, -2, -2, 1, -4, 4, -2, 3, -3, 1, 3, 1, -16, -2, -2, -2, -7, 1, -2, -2, -4, 1, 3, 1, -3, -5, -2, 1, -4, 6, -9, -2, -3, 1, -12, -2, -4, -2, -2, 1, 5, 1, -2, -5, -48, -2, 3, 1, -3, -2, 3, 1, -8, 1, -2, -9, -3, -2, 3, 1, -4, 0, -2, 1, 5, -2, -2, -2, -4
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OFFSET
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1,6
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LINKS
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FORMULA
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MATHEMATICA
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f[p_, e_] := e/p; d[1] = 0; d[n_] := n*Plus @@ f @@@ FactorInteger[n]; a[n_] := DivisorSum[n, MoebiusMu[#] * DivisorSigma[1, #] * d[n/#] &]; Array[a, 100] (* Amiram Eldar, Nov 25 2021 *)
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PROG
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(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A063441(n) = (moebius(n)*sigma(n)); \\ Also Dirichlet inverse of A003959.
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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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