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A144845 Least number k such that all coefficients of k*B(n,x), the n-th 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 (list; graph; refs; listen; history; text; internal format)
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), 117-123.

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

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Last modified December 4 21:09 EST 2016. Contains 278755 sequences.