A note on the denominators of Bernoulli numbers
Journal
Proceedings of the Japan Academy, Series A, Mathematical Sciences
ISSN
0386-2194
Date Issued
2014
Author(s)
Type
text::journal::journal article
Abstract
We show that
gcd
(
2
!
S
(
2
n
+
1
,
2
)
,
…
,
(
2
n
+
1
)
!
S
(
2
n
+
1
,
2
n
+
1
)
)
=
denominator of
B
2
n
,
where
S
(
n
,
k
)
is the Stirling number of the second kind and
B
n
is the Bernoulli number.
gcd
(
2
!
S
(
2
n
+
1
,
2
)
,
…
,
(
2
n
+
1
)
!
S
(
2
n
+
1
,
2
n
+
1
)
)
=
denominator of
B
2
n
,
where
S
(
n
,
k
)
is the Stirling number of the second kind and
B
n
is the Bernoulli number.