diff --git a/pandas/core/dtypes/missing.py b/pandas/core/dtypes/missing.py
index 38553bc1be8d6..c457b52cf4b0e 100644
--- a/pandas/core/dtypes/missing.py
+++ b/pandas/core/dtypes/missing.py
@@ -169,13 +169,17 @@ def _isna(obj, inf_as_na: bool = False):
         return False
     elif isinstance(obj, (np.ndarray, ABCExtensionArray)):
         return _isna_array(obj, inf_as_na=inf_as_na)
-    elif isinstance(obj, (ABCSeries, ABCIndex)):
+    elif isinstance(obj, ABCIndex):
+        # Try to use cached isna, which also short-circuits for integer dtypes
+        #  and avoids materializing RangeIndex._values
+        if not obj._can_hold_na:
+            return obj.isna()
+        return _isna_array(obj._values, inf_as_na=inf_as_na)
+
+    elif isinstance(obj, ABCSeries):
         result = _isna_array(obj._values, inf_as_na=inf_as_na)
         # box
-        if isinstance(obj, ABCSeries):
-            result = obj._constructor(
-                result, index=obj.index, name=obj.name, copy=False
-            )
+        result = obj._constructor(result, index=obj.index, name=obj.name, copy=False)
         return result
     elif isinstance(obj, ABCDataFrame):
         return obj.isna()
diff --git a/pandas/core/indexes/range.py b/pandas/core/indexes/range.py
index 8aedc56d8e1cd..aed7a7a467db3 100644
--- a/pandas/core/indexes/range.py
+++ b/pandas/core/indexes/range.py
@@ -496,6 +496,7 @@ def argsort(self, *args, **kwargs) -> npt.NDArray[np.intp]:
         numpy.ndarray.argsort
         """
         ascending = kwargs.pop("ascending", True)  # EA compat
+        kwargs.pop("kind", None)  # e.g. "mergesort" is irrelevant
         nv.validate_argsort(args, kwargs)
 
         if self._range.step > 0:
diff --git a/pandas/tests/indexes/common.py b/pandas/tests/indexes/common.py
index 8f37413dd53c8..e34620d4caf17 100644
--- a/pandas/tests/indexes/common.py
+++ b/pandas/tests/indexes/common.py
@@ -333,11 +333,9 @@ def test_numpy_argsort(self, index):
         expected = index.argsort()
         tm.assert_numpy_array_equal(result, expected)
 
-        if not isinstance(index, RangeIndex):
-            # TODO: add compatibility to RangeIndex?
-            result = np.argsort(index, kind="mergesort")
-            expected = index.argsort(kind="mergesort")
-            tm.assert_numpy_array_equal(result, expected)
+        result = np.argsort(index, kind="mergesort")
+        expected = index.argsort(kind="mergesort")
+        tm.assert_numpy_array_equal(result, expected)
 
         # these are the only two types that perform
         # pandas compatibility input validation - the