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A349445
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Dirichlet convolution of A001511 (the 2-adic valuation of 2n) with A349134 (the Dirichlet inverse of Kimberling's paraphrases).
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5
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1, 1, -1, 1, -2, -1, -3, 1, -2, -2, -5, -1, -6, -3, 0, 1, -8, -2, -9, -2, 0, -5, -11, -1, -6, -6, -4, -3, -14, 0, -15, 1, 0, -8, 0, -2, -18, -9, 0, -2, -20, 0, -21, -5, 2, -11, -23, -1, -12, -6, 0, -6, -26, -4, 0, -3, 0, -14, -29, 0, -30, -15, 3, 1, 0, 0, -33, -8, 0, 0, -35, -2, -36, -18, 4, -9, 0, 0, -39, -2, -8
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OFFSET
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1,5
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LINKS
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FORMULA
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MATHEMATICA
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k[n_] := (n / 2^IntegerExponent[n, 2] + 1)/2; kinv[1] = 1; kinv[n_] := kinv[n] = -DivisorSum[n, kinv[#]*k[n/#] &, # < n &]; a[n_] := DivisorSum[n, IntegerExponent[2*#, 2]*kinv[n/#] &]; Array[a, 100] (* Amiram Eldar, Nov 19 2021 *)
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PROG
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(PARI)
A003602(n) = (1+(n>>valuation(n, 2)))/2;
memoA349134 = Map();
A349134(n) = if(1==n, 1, my(v); if(mapisdefined(memoA349134, n, &v), v, v = -sumdiv(n, d, if(d<n, A003602(n/d)*A349134(d), 0)); mapput(memoA349134, 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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