

A286516


a(n) = b(2*n1)/b(2*n) where b(n) = A195441(n1) = denominator(Bernoulli_{n}(x)  Bernoulli_{n}).


9



1, 2, 3, 2, 5, 3, 7, 2, 3, 5, 11, 1, 13, 7, 15, 2, 17, 3, 19, 5, 7, 11, 23, 1, 5, 13, 3, 7, 29, 5, 31, 2, 11, 17, 7, 1, 37, 19, 13, 5, 41, 21, 43, 11, 3, 23, 47, 1, 7, 5, 17, 13, 53, 3, 11, 7, 19, 29, 59, 1, 61, 31, 7, 2, 65, 11, 67, 17, 23, 5, 71, 1, 73, 37
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OFFSET

1,2


COMMENTS

a(n) is an integer for all n, a(n) is odd if n is not a power of 2, a(2^k)=2 for all k>=1, a(n)=1 infinitely often, and a(n)=p infinitely often for every prime p. See Cor. 2 and Cor. 3 in "The denominators of power sums of arithmetic progressions". See also "Powersum denominators".


LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000
B. C. Kellner, On a product of certain primes, arXiv:1705.04303 [math.NT] 2017; J. Number Theory, 179 (2017), 126141.
B. C. Kellner and J. Sondow, Powersum denominators, arXiv:1705.03857 [math.NT], 2017; Amer. Math. Monthly, 124 (2017), 695709.
Bernd C. Kellner and Jonathan Sondow, The denominators of power sums of arithmetic progressions, arXiv:1705.05331 [math.NT] 2017; Integers, 18 (2018), article A95.


FORMULA

a(n) = A195441(2*n2) / A195441(2*n1).


MATHEMATICA

b[n_] := Denominator[ Together[ BernoulliB[n, x]  BernoulliB[n]]]; Table[
b[2 n  1]/b[2 n], {n, 1, 74}]


CROSSREFS

Cf. A027642, A064538, A144845, A195441, A286515, A286517, A286762, A286763.
Sequence in context: A262549 A086287 A253236 * A273289 A090662 A088387
Adjacent sequences: A286513 A286514 A286515 * A286517 A286518 A286519


KEYWORD

nonn


AUTHOR

Bernd C. Kellner and Jonathan Sondow, May 12 2017


STATUS

approved



