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A361019
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Dirichlet inverse of A038712.
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1
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1, -3, -1, 2, -1, 3, -1, 0, 0, 3, -1, -2, -1, 3, 1, 0, -1, 0, -1, -2, 1, 3, -1, 0, 0, 3, 0, -2, -1, -3, -1, 0, 1, 3, 1, 0, -1, 3, 1, 0, -1, -3, -1, -2, 0, 3, -1, 0, 0, 0, 1, -2, -1, 0, 1, 0, 1, 3, -1, 2, -1, 3, 0, 0, 1, -3, -1, -2, 1, -3, -1, 0, -1, 3, 0, -2, 1, -3, -1, 0, 0, 3, -1, 2, 1, 3, 1, 0, -1, 0, 1, -2, 1, 3, 1, 0, -1
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A038712(n/d) * a(d).
Multiplicative with a(2) = -3, a(2^2) = 2, and a(2^e) = 0 for e > 2, and for odd prime p, a(p)= -1 and a(p^e) = 0 for e > 1. - Amiram Eldar, Mar 02 2023
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MATHEMATICA
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f[p_, e_] := If[e == 1, -1, 0]; f[2, e_] := If[e < 3, If[e == 1, -3, 2], 0]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Mar 02 2023 *)
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PROG
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(PARI)
A038712(n) = ((1<<(1+valuation(n, 2)))-1);
memoA361019 = Map();
A361019(n) = if(1==n, 1, my(v); if(mapisdefined(memoA361019, n, &v), v, v = -sumdiv(n, d, if(d<n, A038712(n/d)*A361019(d), 0)); mapput(memoA361019, n, v); (v)));
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CROSSREFS
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KEYWORD
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sign,mult
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AUTHOR
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STATUS
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approved
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