diff --git a/pandas/_libs/tslibs/offsets.pyx b/pandas/_libs/tslibs/offsets.pyx
index 856aa52f82cf55..e28462f7103b95 100644
--- a/pandas/_libs/tslibs/offsets.pyx
+++ b/pandas/_libs/tslibs/offsets.pyx
@@ -18,6 +18,7 @@ from numpy cimport int64_t
 cnp.import_array()
 
 
+from pandas._libs.tslibs cimport util
 from pandas._libs.tslibs.util cimport is_string_object, is_integer_object
 
 from pandas._libs.tslibs.ccalendar import MONTHS, DAYS
@@ -408,6 +409,10 @@ class _BaseOffset(object):
         return self.apply(other)
 
     def __mul__(self, other):
+        if hasattr(other, "_typ"):
+            return NotImplemented
+        if util.is_array(other):
+            return np.array([self * x for x in other])
         return type(self)(n=other * self.n, normalize=self.normalize,
                           **self.kwds)
 
@@ -458,6 +463,9 @@ class _BaseOffset(object):
         TypeError if `int(n)` raises
         ValueError if n != int(n)
         """
+        if util.is_timedelta64_object(n):
+            raise TypeError('`n` argument must be an integer, '
+                            'got {ntype}'.format(ntype=type(n)))
         try:
             nint = int(n)
         except (ValueError, TypeError):
@@ -533,12 +541,20 @@ class _Tick(object):
     can do isinstance checks on _Tick and avoid importing tseries.offsets
     """
 
+    # ensure that reversed-ops with numpy scalars return NotImplemented
+    __array_priority__ = 1000
+
     def __truediv__(self, other):
         result = self.delta.__truediv__(other)
         return _wrap_timedelta_result(result)
 
+    def __rtruediv__(self, other):
+        result = self.delta.__rtruediv__(other)
+        return _wrap_timedelta_result(result)
+
     if PY2:
         __div__ = __truediv__
+        __rdiv__ = __rtruediv__
 
 
 # ----------------------------------------------------------------------
diff --git a/pandas/tests/tseries/offsets/test_offsets.py b/pandas/tests/tseries/offsets/test_offsets.py
index ac3955970587fe..621572da575416 100644
--- a/pandas/tests/tseries/offsets/test_offsets.py
+++ b/pandas/tests/tseries/offsets/test_offsets.py
@@ -257,6 +257,26 @@ def test_offset_n(self, offset_types):
         mul_offset = offset * 3
         assert mul_offset.n == 3
 
+    def test_offset_timedelta64_arg(self, offset_types):
+        # check that offset._validate_n raises TypeError on a timedelt64
+        #  object
+        off = self._get_offset(offset_types)
+
+        td64 = np.timedelta64(4567, 's')
+        with pytest.raises(TypeError, match="argument must be an integer"):
+            type(off)(n=td64, **off.kwds)
+
+    def test_offset_mul_ndarray(self, offset_types):
+        off = self._get_offset(offset_types)
+
+        expected = np.array([[off, off * 2], [off * 3, off * 4]])
+
+        result = np.array([[1, 2], [3, 4]]) * off
+        tm.assert_numpy_array_equal(result, expected)
+
+        result = off * np.array([[1, 2], [3, 4]])
+        tm.assert_numpy_array_equal(result, expected)
+
     def test_offset_freqstr(self, offset_types):
         offset = self._get_offset(offset_types)
 
diff --git a/pandas/tests/tseries/offsets/test_ticks.py b/pandas/tests/tseries/offsets/test_ticks.py
index f4b012ec1897f9..9a8251201f75fa 100644
--- a/pandas/tests/tseries/offsets/test_ticks.py
+++ b/pandas/tests/tseries/offsets/test_ticks.py
@@ -11,6 +11,7 @@
 import pytest
 
 from pandas import Timedelta, Timestamp
+import pandas.util.testing as tm
 
 from pandas.tseries import offsets
 from pandas.tseries.offsets import Hour, Micro, Milli, Minute, Nano, Second
@@ -262,6 +263,28 @@ def test_tick_division(cls):
         assert result.delta == off.delta / .001
 
 
+@pytest.mark.parametrize('cls', tick_classes)
+def test_tick_rdiv(cls):
+    off = cls(10)
+    delta = off.delta
+    td64 = delta.to_timedelta64()
+
+    with pytest.raises(TypeError):
+        2 / off
+    with pytest.raises(TypeError):
+        2.0 / off
+
+    assert (td64 * 2.5) / off == 2.5
+
+    if cls is not Nano:
+        # skip pytimedelta for Nano since it gets dropped
+        assert (delta.to_pytimedelta() * 2) / off == 2
+
+    result = np.array([2 * td64, td64]) / off
+    expected = np.array([2., 1.])
+    tm.assert_numpy_array_equal(result, expected)
+
+
 @pytest.mark.parametrize('cls1', tick_classes)
 @pytest.mark.parametrize('cls2', tick_classes)
 def test_tick_zero(cls1, cls2):