This site is supported by donations to The OEIS Foundation.

"Email this user" was broken Aug 14 to 9am Aug 16. If you sent someone a message in this period, please send it again.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A144845 Least number k such that all coefficients of k*B(n,x), the n-th Bernoulli polynomial, are integers. 11
 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 In "The denominators of power sums of arithmetic progressions" Corollary 1, we give a simple way to compute a(n) without using Bernoulli polynomials. Namely, a(n) equals (product of the primes dividing n+1) times (product of the primes p <= (n+1)/(2+(n+1 mod 2)) not dividing n+1 such that the sum of the base-p digits of n+1 is at least p). - Bernd C. Kellner and Jonathan Sondow, May 15 2017 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. Bernd C. Kellner and Jonathan Sondow, Power-Sum Denominators, arXiv:1705.03857 [math.NT] 2017, to appear in Amer. Math. Monthly. Bernd C. Kellner and Jonathan Sondow, The denominators of power sums of arithmetic progressions, arXiv:1705.05331 [math.NT], submitted 2017. 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 Cf. A027642, A064538, A144845, A195441, A286515, A286516, A286517. Sequence in context: A141498 A284004 A225481 * A200563 A284577 A122018 Adjacent sequences:  A144842 A144843 A144844 * A144846 A144847 A144848 KEYWORD nonn AUTHOR T. D. Noe, Sep 22 2008 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.