We will use p to refer to phi.
p + p2 + p4 + p6 + ... + p142 + p144 = pn
One property of phi is that 1 + p = p2.
From this, p + p2 = p3.
So in the problem, we can replace p + p2 with p3 to get
p3 + p4 + p6 + ... + p142 + p144 = pn.
Since 1 + p = p2, again, p3 + p4 = p5, and in general, pn + pn+1 = pn+2.
If we continue the process...
p141 + p142 + p144 = pn
p143 + p144 = pn
p145 = pn
So n = 145.
Solution by lizard-socks (which happens to solve every variation of this problem):
