Euler totient asymptotic via Riemann zeta function

N[Table[(Re[
      Sum[Total[MoebiusMu[Divisors[n]]/Divisors[n]]/n, {n, 1,
        nn + 1}]] -
     Re[Sum[Total[MoebiusMu[Divisors[n]]/Divisors[n]]/n, {n, 1,
        nn}]])*(nn + 1)^2, {nn, 1, 60}]]
g1 = ListLinePlot[%]
N[Table[(Re[Zeta[1 + 1/Log[nn + 1]]/Zeta[1 + 1 + 1/Log[nn + 1]]] -
     Re[Zeta[1 + 1/Log[nn]]/Zeta[1 + 1 + 1/Log[nn]]])*(nn + 1)^2, {nn,
    1, 60}]]
g2 = ListLinePlot[%]
Show[g1, g2]
EulerPhi[Range[60] + 1]