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I guess this is because euler_phi does not accept symbolic argument
sage: var('z')
sage: euler_phi(z)
Traceback (most recent call last):
...
PariError: not an integer argument in an arithmetic function (18)
Nevertheless, you can do
sage: sum((euler_phi(k)/k)*log(1/(1-2*z^k)) for k in xrange(2,5))
1/2*log(-1/(2*z^4 - 1)) + 2/3*log(-1/(2*z^3 - 1)) + 1/2*log(-1/(2*z^2 - 1))
