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A119766
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Numbers n such that numerator of Bernoulli(n)/n is (apart from sign) 1 or a prime.
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3
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1, 2, 4, 6, 8, 10, 12, 14, 16, 18, 26, 34, 36, 38, 42, 74, 114, 118, 396, 674, 1870, 4306, 22808
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OFFSET
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1,2
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COMMENTS
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In 1911 Ramanujan believed that the numerator of Bernoulli(n)/n for n even was (apart from sign) always either 1 or a prime. This is false.
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REFERENCES
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S. Ramanujan, Some properties of Bernoulli's numbers, J. Indian Math. Soc., 3 (1911), 219-234.
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LINKS
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EXAMPLE
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As an example, Bernoulli(20)/20 = -174611/6600, but 174611 = 283*617. - Robert G. Wilson v, Jun 22 2006
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MAPLE
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A119766 := proc(nmax) local numr; for n from 2 to nmax by 2 do numr := abs(numer(bernoulli(n)/n)) ; if numr = 1 or isprime(numr) then print(n) ; fi ; od ; end : A119766(2000) ; # R. J. Mathar, Jun 21 2006
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MATHEMATICA
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OldPrimeQ[n_] := Abs[n]==1 || PrimeQ[Abs[n]]; Select[Range[2000], OldPrimeQ[Numerator[BernoulliB[ # ]/# ]] &] (* T. D. Noe, Jun 20 2006 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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