diff --git a/pandas/core/indexes/range.py b/pandas/core/indexes/range.py
index f37faa4ab844b..b0911cc0ce556 100644
--- a/pandas/core/indexes/range.py
+++ b/pandas/core/indexes/range.py
@@ -46,6 +46,7 @@
 from pandas.core.indexes.numeric import (
     Float64Index,
     Int64Index,
+    NumericIndex,
 )
 from pandas.core.ops.common import unpack_zerodim_and_defer
 
@@ -55,7 +56,7 @@
 _empty_range = range(0)
 
 
-class RangeIndex(Int64Index):
+class RangeIndex(NumericIndex):
     """
     Immutable Index implementing a monotonic integer range.
 
@@ -97,6 +98,7 @@ class RangeIndex(Int64Index):
 
     _typ = "rangeindex"
     _engine_type = libindex.Int64Engine
+    _can_hold_na = False
     _range: range
 
     # --------------------------------------------------------------------
@@ -381,6 +383,10 @@ def __contains__(self, key: Any) -> bool:
             return False
         return key in self._range
 
+    @property
+    def inferred_type(self) -> str:
+        return "integer"
+
     # --------------------------------------------------------------------
     # Indexing Methods
 
diff --git a/pandas/io/feather_format.py b/pandas/io/feather_format.py
index 3999f91a7b141..d032c54395c6d 100644
--- a/pandas/io/feather_format.py
+++ b/pandas/io/feather_format.py
@@ -56,7 +56,7 @@ def to_feather(
     # validate that we have only a default index
     # raise on anything else as we don't serialize the index
 
-    if not isinstance(df.index, Int64Index):
+    if not isinstance(df.index, (Int64Index, RangeIndex)):
         typ = type(df.index)
         raise ValueError(
             f"feather does not support serializing {typ} "
diff --git a/pandas/tests/indexes/common.py b/pandas/tests/indexes/common.py
index e5a24e9b938e2..ab2b2db7eec53 100644
--- a/pandas/tests/indexes/common.py
+++ b/pandas/tests/indexes/common.py
@@ -516,7 +516,7 @@ def test_hasnans_isnans(self, index_flat):
             return
         elif isinstance(index, DatetimeIndexOpsMixin):
             values[1] = iNaT
-        elif isinstance(index, (Int64Index, UInt64Index)):
+        elif isinstance(index, (Int64Index, UInt64Index, RangeIndex)):
             return
         else:
             values[1] = np.nan
@@ -555,7 +555,7 @@ def test_fillna(self, index):
 
             if isinstance(index, DatetimeIndexOpsMixin):
                 values[1] = iNaT
-            elif isinstance(index, (Int64Index, UInt64Index)):
+            elif isinstance(index, (Int64Index, UInt64Index, RangeIndex)):
                 return
             else:
                 values[1] = np.nan
diff --git a/pandas/tests/indexes/test_numpy_compat.py b/pandas/tests/indexes/test_numpy_compat.py
index 1ee7c5547ecf9..59c30c3abac03 100644
--- a/pandas/tests/indexes/test_numpy_compat.py
+++ b/pandas/tests/indexes/test_numpy_compat.py
@@ -12,6 +12,7 @@
     Index,
     Int64Index,
     PeriodIndex,
+    RangeIndex,
     TimedeltaIndex,
     UInt64Index,
 )
@@ -55,7 +56,7 @@ def test_numpy_ufuncs_basic(index, func):
         with tm.external_error_raised((TypeError, AttributeError)):
             with np.errstate(all="ignore"):
                 func(index)
-    elif isinstance(index, (Float64Index, Int64Index, UInt64Index)):
+    elif isinstance(index, (Float64Index, Int64Index, UInt64Index, RangeIndex)):
         # coerces to float (e.g. np.sin)
         with np.errstate(all="ignore"):
             result = func(index)
@@ -104,7 +105,7 @@ def test_numpy_ufuncs_other(index, func, request):
         with tm.external_error_raised(TypeError):
             func(index)
 
-    elif isinstance(index, (Float64Index, Int64Index, UInt64Index)):
+    elif isinstance(index, (Float64Index, Int64Index, UInt64Index, RangeIndex)):
         # Results in bool array
         result = func(index)
         assert isinstance(result, np.ndarray)