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%I #34 Jul 03 2022 06:47:21
%S 3,5,7,3,11,13,5,17,19,7,23,5,3,29,31,11,35,37,13,41,43,1,47,7,17,53,
%T 55,19,59,61,7,13,67,23,71,73,5,77,79,3,83,17,29,89,13,31,19,97,11,
%U 101,103,7,107,109,37,113,23,13,119,11,41,5,127,43,131,19,5
%N a(n) = b(2*n)/b(2*n+1) where b(n) = denominator(Bernoulli_{n}(x)).
%C a(n) is an odd integer for all n, a(n)=1 infinitely often, and a(n)=p infinitely often for every odd prime p. See Cor. 2 and Cor. 3 in "The denominators of power sums of arithmetic progressions". See also "Power-sum denominators".
%H G. C. Greubel, <a href="/A286517/b286517.txt">Table of n, a(n) for n = 1..1000</a>
%H Bernd C. Kellner, <a href="https://doi.org/10.1016/j.jnt.2017.03.020">On a product of certain primes</a>, J. Number Theory, 179 (2017), 126-141; arXiv:<a href="https://arxiv.org/abs/1705.04303">1705.04303</a> [math.NT], 2017.
%H Bernd C. Kellner and Jonathan Sondow, <a href="https://doi.org/10.4169/amer.math.monthly.124.8.695">Power-Sum Denominators</a>, Amer. Math. Monthly, 124 (2017), 695-709; arXiv:<a href="https://arxiv.org/abs/1705.03857">1705.03857</a> [math.NT], 2017.
%H Bernd C. Kellner and Jonathan Sondow, <a href="http://math.colgate.edu/~integers/s95/s95.pdf">The denominators of power sums of arithmetic progressions</a>, Integers 18 (2018), #A95, 17 pp.; arXiv:<a href="https://arxiv.org/abs/1705.05331">1705.05331</a> [math.NT], 2017.
%F a(n) = A144845(2*n) / A144845(2*n+1) for n >= 1.
%t b[n_] := Denominator[ Together[ BernoulliB[n, x]]]; Table[ b[2 n]/b[2 n + 1], {n, 1, 67}]
%Y Cf. A027642, A064538, A144845, A195441, A286515, A286516.
%K nonn
%O 1,1
%A _Bernd C. Kellner_ and _Jonathan Sondow_, May 12 2017
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