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A051229
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Numbers m such that the Bernoulli number B_{2*m} has denominator 66.
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36
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5, 25, 85, 185, 235, 295, 305, 335, 355, 365, 395, 425, 505, 535, 635, 685, 695, 745, 815, 835, 925, 985, 995, 1115, 1135, 1145, 1285, 1315, 1345, 1385, 1415, 1445, 1475, 1525, 1535, 1555, 1565, 1585, 1655, 1675, 1735, 1765
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OFFSET
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1,1
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COMMENTS
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From the von Staudt-Clausen theorem, denominator(B_{2*m}) = product of primes p such that (p-1)|2*m.
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REFERENCES
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B. C. Berndt, Ramanujan's Notebooks Part IV, Springer-Verlag, see p. 75.
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LINKS
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FORMULA
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EXAMPLE
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The numbers m = 5, 25 belong to the list because B_10 = 5/66 and B_50 = 495057205241079648212477525/66. - Petros Hadjicostas, Jun 06 2020
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MATHEMATICA
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Select[Range[2000], Denominator[BernoulliB[2 #]]==66&] (* Harvey P. Dale, Mar 11 2012 *)
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PROG
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(Sage) [n for n in (1..2000) if denominator(bernoulli(2*n))==66 ] # G. C. Greubel, Jun 06 2020
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CROSSREFS
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KEYWORD
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nonn,nice,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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