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A349914
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Sum of A000593 (the sum of odd divisors function) and its Dirichlet inverse.
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3
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2, 0, 0, 1, 0, 8, 0, 1, 16, 12, 0, 4, 0, 16, 48, 1, 0, 10, 0, 6, 64, 24, 0, 4, 36, 28, 40, 8, 0, 0, 0, 1, 96, 36, 96, 13, 0, 40, 112, 6, 0, 0, 0, 12, 60, 48, 0, 4, 64, 26, 144, 14, 0, 40, 144, 8, 160, 60, 0, 24, 0, 64, 80, 1, 168, 0, 0, 18, 192, 0, 0, 13, 0, 76, 104, 20, 192, 0, 0, 6, 121, 84, 0, 32, 216, 88, 240
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OFFSET
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1,1
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LINKS
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FORMULA
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a(1) = 2, and for n > 1, a(n) = -Sum_{d|n, 1<d<n} A000593(d) * A327278(n/d).
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MATHEMATICA
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f1[p_, e_] := If[p==2, 1, (p^(e+1)-1)/(p-1)]; f2[p_, e_] := If[p == 2, -Boole[e == 1], Which[e == 1, -p - 1, e == 2, p, e > 2, 0]]; a[1] = 2; a[n_] := Times @@ f1 @@@ (f = FactorInteger[n]) + Times @@ f2 @@@ f; Array[a, 100] (* Amiram Eldar, Dec 08 2021 *)
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PROG
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(PARI)
A000593(n) = sigma(n>>valuation(n, 2));
A327278(n) = sumdiv(n, d, if(d%2, d*moebius(d)*moebius(n/d), 0));
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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