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A318320
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a(n) = (psi(n) - phi(n))/2.
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6
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0, 1, 1, 2, 1, 5, 1, 4, 3, 7, 1, 10, 1, 9, 8, 8, 1, 15, 1, 14, 10, 13, 1, 20, 5, 15, 9, 18, 1, 32, 1, 16, 14, 19, 12, 30, 1, 21, 16, 28, 1, 42, 1, 26, 24, 25, 1, 40, 7, 35, 20, 30, 1, 45, 16, 36, 22, 31, 1, 64, 1, 33, 30, 32, 18, 62, 1, 38, 26, 60, 1, 60, 1, 39, 40, 42, 18, 72, 1, 56, 27, 43, 1, 84, 22, 45, 32, 52, 1, 96
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OFFSET
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1,4
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LINKS
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FORMULA
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Sum_{k=1..n} a(k) = c * n^2 + O(n*log(n)), where c = 9/(4*Pi^2) = 0.227972... . - Amiram Eldar, Dec 05 2023
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MATHEMATICA
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psi[n_] := n * Times @@ (1 + 1/FactorInteger[n][[;; , 1]]); psi[1] = 1; a[n_] := (psi[n] - EulerPhi[n])/2; Array[a, 100] (* Amiram Eldar, Dec 05 2023 *)
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PROG
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(PARI) A318320(n) = sumdiv(n, d, (-1==moebius(n/d))*d);
(PARI) A318320(n) = ((n*sumdivmult(n, d, issquarefree(d)/d))-eulerphi(n))/2;
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CROSSREFS
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Differs from A069359 for the first time at n=30, where a(30) = 32, while A069359(30) = 31.
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KEYWORD
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AUTHOR
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STATUS
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approved
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