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A286515
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a(n) = denominator(Bernoulli_{n}(x)) / denominator(Bernoulli_{n}).
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5
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1, 1, 1, 2, 1, 6, 1, 6, 1, 10, 1, 6, 1, 210, 5, 6, 1, 30, 5, 210, 7, 330, 5, 30, 1, 546, 7, 14, 1, 30, 1, 462, 77, 3570, 35, 6, 1, 51870, 455, 210, 7, 2310, 55, 2310, 7, 4830, 35, 210, 1, 6630, 221, 858, 11, 330, 55, 798, 19, 870, 5, 30, 1, 930930, 5005, 4290
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OFFSET
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0,4
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COMMENTS
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a(n) is a squarefree integer for all n, a(n) is odd if n>=0 is even, and a(n) is even if n>=3 is odd. See "Power-sum denominators", Thm. 4, pp. 12-13, and "The denominators of power sums of arithmetic progressions", Thm. 3, pp. 3 and 11-12.
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LINKS
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FORMULA
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MAPLE
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seq(denom(bernoulli(n, x))/denom(bernoulli(n)), n=0..100); # Robert Israel, May 24 2017
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MATHEMATICA
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Table[ Denominator[ Together[ BernoulliB[n, x]]]/Denominator[ BernoulliB[n]], {n, 0, 63}]
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PROG
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(PARI) apply( a(n)=denominator(content(bernpol(n)))/denominator(bernfrac(n)), [1..50]) \\ M. F. Hasler, Dec 10 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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