  Trends in the planet population with host star mass provide an avenue to
constrain planet formation theories. We derive the planet radius distribution
function for Kepler stars of different spectral types, sampling a range in host
star masses. We find that M dwarf stars have 3.5 times more small planets
(1.0-2.8 R_Earth) than main-sequence FGK stars, but two times fewer
Neptune-sized and larger planets (>2.8 R_Earth). We find no systematic trend in
the planet size distribution between spectral types F, G, and K to explain the
increasing occurrence rates. Taking into account the mass-radius relationship
and heavy-element mass of observed exoplanets, and assuming those are
independent of spectral type, we derive the inventory of the heavy-element mass
locked up in exoplanets at short orbits. The overall higher planet occurrence
rates around M stars are not consistent with the redistribution of the same
mass into more, smaller planets. At the orbital periods and planet radii where
Kepler observations are complete for all spectral types, the average
heavy-element mass locked up in exoplanets increases roughly inversely with
stellar mass from 4 M_Earth in F stars to 5 M_Earth in G and K stars to 7
M_Earth in M stars. This trend stands in stark contrast with observed
protoplanetary disk masses that decrease towards lower mass stars, and provides
a challenge for current planet formation models. Neither models of in situ
formation nor migration of fully-formed planets are consistent with these
results. Instead, these results are indicative of large-scale inward migration
of planetary building blocks --- either through type-I migration or radial
drift of dust grains --- that is more efficient for lower mass stars, but does
not result in significantly larger or smaller planets.
