diff --git a/pandas/_libs/tslibs/timedeltas.pyx b/pandas/_libs/tslibs/timedeltas.pyx
index 8eaf86b3d193f..f8f8a6f81d801 100644
--- a/pandas/_libs/tslibs/timedeltas.pyx
+++ b/pandas/_libs/tslibs/timedeltas.pyx
@@ -173,11 +173,11 @@ cpdef int64_t delta_to_nanoseconds(delta) except? -1:
     if is_tick_object(delta):
         return delta.nanos
     if isinstance(delta, _Timedelta):
-        delta = delta.value
+        return delta.value
+
     if is_timedelta64_object(delta):
         return get_timedelta64_value(ensure_td64ns(delta))
-    if is_integer_object(delta):
-        return delta
+
     if PyDelta_Check(delta):
         try:
             return (
diff --git a/pandas/core/arrays/datetimelike.py b/pandas/core/arrays/datetimelike.py
index 7a7bad02fde72..e070f23b35315 100644
--- a/pandas/core/arrays/datetimelike.py
+++ b/pandas/core/arrays/datetimelike.py
@@ -1316,7 +1316,9 @@ def __add__(self, other):
         elif is_integer_dtype(other_dtype):
             if not is_period_dtype(self.dtype):
                 raise integer_op_not_supported(self)
-            result = cast("PeriodArray", self)._addsub_int_array(other, operator.add)
+            result = cast("PeriodArray", self)._addsub_int_array_or_scalar(
+                other, operator.add
+            )
         else:
             # Includes Categorical, other ExtensionArrays
             # For PeriodDtype, if self is a TimedeltaArray and other is a
@@ -1376,7 +1378,9 @@ def __sub__(self, other):
         elif is_integer_dtype(other_dtype):
             if not is_period_dtype(self.dtype):
                 raise integer_op_not_supported(self)
-            result = cast("PeriodArray", self)._addsub_int_array(other, operator.sub)
+            result = cast("PeriodArray", self)._addsub_int_array_or_scalar(
+                other, operator.sub
+            )
         else:
             # Includes ExtensionArrays, float_dtype
             return NotImplemented
diff --git a/pandas/core/arrays/period.py b/pandas/core/arrays/period.py
index 2368af0de1bf3..b2a8dfddc6b68 100644
--- a/pandas/core/arrays/period.py
+++ b/pandas/core/arrays/period.py
@@ -747,8 +747,8 @@ def _sub_period_array(self, other):
             new_values[mask] = NaT
         return new_values
 
-    def _addsub_int_array(
-        self, other: np.ndarray, op: Callable[[Any, Any], Any]
+    def _addsub_int_array_or_scalar(
+        self, other: np.ndarray | int, op: Callable[[Any, Any], Any]
     ) -> PeriodArray:
         """
         Add or subtract array of integers; equivalent to applying
@@ -756,7 +756,7 @@ def _addsub_int_array(
 
         Parameters
         ----------
-        other : np.ndarray[integer-dtype]
+        other : np.ndarray[int64] or int
         op : {operator.add, operator.sub}
 
         Returns
@@ -775,12 +775,7 @@ def _add_offset(self, other: BaseOffset):
         assert not isinstance(other, Tick)
 
         self._require_matching_freq(other, base=True)
-
-        # Note: when calling parent class's _add_timedeltalike_scalar,
-        #  it will call delta_to_nanoseconds(delta).  Because delta here
-        #  is an integer, delta_to_nanoseconds will return it unchanged.
-        result = super()._add_timedeltalike_scalar(other.n)
-        return type(self)(result, freq=self.freq)
+        return self._addsub_int_array_or_scalar(other.n, operator.add)
 
     def _add_timedeltalike_scalar(self, other):
         """
@@ -800,10 +795,8 @@ def _add_timedeltalike_scalar(self, other):
             # special handling for np.timedelta64("NaT"), avoid calling
             #  _check_timedeltalike_freq_compat as that would raise TypeError
             other = self._check_timedeltalike_freq_compat(other)
+            other = np.timedelta64(other, "ns")
 
-        # Note: when calling parent class's _add_timedeltalike_scalar,
-        #  it will call delta_to_nanoseconds(delta).  Because delta here
-        #  is an integer, delta_to_nanoseconds will return it unchanged.
         return super()._add_timedeltalike_scalar(other)
 
     def _add_timedelta_arraylike(self, other):
@@ -828,7 +821,7 @@ def _add_timedelta_arraylike(self, other):
             # all-NaT TimedeltaIndex is equivalent to a single scalar td64 NaT
             return self + np.timedelta64("NaT")
 
-        ordinals = self._addsub_int_array(delta, operator.add).asi8
+        ordinals = self._addsub_int_array_or_scalar(delta, operator.add).asi8
         return type(self)(ordinals, dtype=self.dtype)
 
     def _check_timedeltalike_freq_compat(self, other):
diff --git a/pandas/core/indexes/period.py b/pandas/core/indexes/period.py
index a296ce130bbf5..fc7b122689ebb 100644
--- a/pandas/core/indexes/period.py
+++ b/pandas/core/indexes/period.py
@@ -272,7 +272,7 @@ def __new__(
     def values(self) -> np.ndarray:
         return np.asarray(self, dtype=object)
 
-    def _maybe_convert_timedelta(self, other):
+    def _maybe_convert_timedelta(self, other) -> int | npt.NDArray[np.int64]:
         """
         Convert timedelta-like input to an integer multiple of self.freq
 
diff --git a/pandas/tests/tslibs/test_timedeltas.py b/pandas/tests/tslibs/test_timedeltas.py
index a0ec563d1f48f..7d7de7492a07b 100644
--- a/pandas/tests/tslibs/test_timedeltas.py
+++ b/pandas/tests/tslibs/test_timedeltas.py
@@ -30,9 +30,6 @@
             24 * 3600e9 + 111,
         ),  # GH43764
         (offsets.Nano(125), 125),
-        (1, 1),
-        (np.int64(2), 2),
-        (np.int32(3), 3),
     ],
 )
 def test_delta_to_nanoseconds(obj, expected):
@@ -46,6 +43,15 @@ def test_delta_to_nanoseconds_error():
     with pytest.raises(TypeError, match="<class 'numpy.ndarray'>"):
         delta_to_nanoseconds(obj)
 
+    with pytest.raises(TypeError, match="float"):
+        delta_to_nanoseconds(1.5)
+    with pytest.raises(TypeError, match="int"):
+        delta_to_nanoseconds(1)
+    with pytest.raises(TypeError, match="int"):
+        delta_to_nanoseconds(np.int64(2))
+    with pytest.raises(TypeError, match="int"):
+        delta_to_nanoseconds(np.int32(3))
+
 
 def test_huge_nanoseconds_overflow():
     # GH 32402