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A349612
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Dirichlet convolution of A342001 [{arithmetic derivative of n}/A003557(n)] with A325126 [Dirichlet inverse of rad(n)].
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4
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0, 1, 1, 0, 1, 0, 1, 1, -1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, -3, 0, 3, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, -5, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, -5, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0
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OFFSET
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1,25
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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]; f1[p_, e_] := p^(e-1); s1[1] = 1; s1[n_] := Times @@ f1 @@@ FactorInteger[n]; f2[p_, e_] := -p*(1 - p)^(e - 1); s2[1] = 1; s2[n_] := Times @@ f2 @@@ FactorInteger[n]; a[n_] := DivisorSum[n, d[#]*s2[n/#]/s1[#] &]; Array[a, 100] (* Amiram Eldar, Nov 23 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]));
A003557(n) = (n/factorback(factorint(n)[, 1]));
memoA325126 = Map();
A325126(n) = if(1==n, 1, my(v); if(mapisdefined(memoA325126, n, &v), v, v = -sumdiv(n, d, if(d<n, A007947(n/d)*A325126(d), 0)); mapput(memoA325126, n, v); (v)));
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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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