

A144845


Least number k such that all coefficients of k*B(n,x), the nth Bernoulli polynomial, are integers.


8



1, 2, 6, 2, 30, 6, 42, 6, 30, 10, 66, 6, 2730, 210, 30, 6, 510, 30, 3990, 210, 2310, 330, 690, 30, 2730, 546, 42, 14, 870, 30, 14322, 462, 39270, 3570, 210, 6, 1919190, 51870, 2730, 210, 94710, 2310, 99330, 2310, 4830, 4830, 9870, 210, 46410, 6630, 14586, 858
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OFFSET

0,2


COMMENTS

The lcm of the terms in row n of A053383. It appears that the Bernoulli polynomial B(n,x) is irreducible for all even n.
This sequence appears in a paper of Bazsó & Mező who use this sequence to give necessary and sufficient condition for power sums to be integer polynomials.  Istvan Mezo, Mar 20 2016


LINKS

T. D. Noe, Table of n, a(n) for n = 0..1000
András Bazsó and István Mező, On the coefficients of power sums of arithmetic progressions, J. Number Th., 153 (2015), 117123.
Eric W. Weisstein, The World of Mathematics: Bernoulli Polynomial


MAPLE

seq(denom(bernoulli(i, x)), i=0..51); # Peter Luschny, Jun 16 2012


MATHEMATICA

Join[{1}, Table[1/FactorTerms[BernoulliB[n, x], x][[1]], {n, 100}]]


CROSSREFS

Sequence in context: A141056 A141498 A225481 * A200563 A122018 A005729
Adjacent sequences: A144842 A144843 A144844 * A144846 A144847 A144848


KEYWORD

nonn


AUTHOR

T. D. Noe, Sep 22 2008


STATUS

approved



