I'm not familiar with any 1- or 2-spool engines that have only the fan on N1. Which engines are so designed?
The military TF34 is one, and the early CF34's too: Single-stage fan driven by a 4-stage LP turbine, and a 14-stage HP compressor and 2-stage HP turbine core. Said core is a scaled-up version of the T64 helo & turboprop engine.
Note the CF34-8 & -10 are altogether different in layout from these original engines.
I'm not aware of any single-spool engines with a fan, which would amount to in effect a "leaky" stage 1 of the compressor.