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Sum_{k=1..n} a(nk) = (Pi^2/12 - 6/Pi^2 + 1/2) * n^2 + O(n*log(n)). - Amiram Eldar, Dec 04 2023
a(n) = (Pi^2/12 - 6/Pi^2 + 1/2) * n^2 + O(n*log(n)). - Amiram Eldar, Dec 04 2023
a[n_] := n + DivisorSigma[1, n] - 2 * EulerPhi[n]; Array[a, 100] (* Amiram Eldar, Dec 04 2023 *)
(PARI) a(n) = {my(f = factor(n)); n + sigma(f) - 2*eulerphi(f); } \\ Amiram Eldar, Dec 04 2023
nonn,easy
a(n) = A000203(n) - A083254(n) = n + ( + A000203(n) - 2*A000010(n)).).
Antti Karttunen, <a href="/A324048/b324048.txt">Table of n, a(n) for n = 1..20000</a>
a(n) = A297159(n) + 2*A001065(n).
Cf. A000010, A000203, A001065, A051709, A051612, A051953, A083254, A297159.
Cf. also A051709, A297159.