A286517 a(n) = b(2*n)/b(2*n+1) where b(n) = denominator(Bernoulli_{n}(x)).

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, 55, 19, 59, 61, 7, 13, 67, 23, 71, 73, 5, 77, 79, 3, 83, 17, 29, 89, 13, 31, 19, 97, 11, 101, 103, 7, 107, 109, 37, 113, 23, 13, 119, 11, 41, 5, 127, 43, 131, 19, 5

Offset: 1

Author

Bernd C. Kellner and Jonathan Sondow, May 12 2017

Keywords

• nonn

Comments

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".

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Bernd C. Kellner, On a product of certain primes, J. Number Theory, 179 (2017), 126-141; arXiv:1705.04303 [math.NT], 2017.
• Bernd C. Kellner and Jonathan Sondow, Power-Sum Denominators, Amer. Math. Monthly, 124 (2017), 695-709; arXiv:1705.03857 [math.NT], 2017.
• Bernd C. Kellner and Jonathan Sondow, The denominators of power sums of arithmetic progressions, Integers 18 (2018), #A95, 17 pp.; arXiv:1705.05331 [math.NT], 2017.

Crossrefs

Cf. A027642, A064538, A144845, A195441, A286515, A286516.

Programs

Mathematica

b[n_] := Denominator[ Together[ BernoulliB[n, x]]]; Table[ b[2 n]/b[2 n + 1], {n, 1, 67}]

Formula

a(n) = A144845(2*n) / A144845(2*n+1) for n >= 1.