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%I #13 Jul 19 2015 04:50:39
%S 1,2,4,6,8,10,12,14,16,18,26,34,36,38,42,74,114,118,396,674,1870,4306,
%T 22808
%N Numbers n such that numerator of Bernoulli(n)/n is (apart from sign) 1 or a prime.
%C 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.
%D S. Ramanujan, Some properties of Bernoulli's numbers, J. Indian Math. Soc., 3 (1911), 219-234.
%H K. Ono, <a href="http://www.ams.org/notices/200606/fea-ono.pdf">Honoring a gift from Kumbakonam</a>, Notices Amer. Math. Soc., 53 (2006), 640-651.
%e As an example, Bernoulli(20)/20 = -174611/6600, but 174611 = 283*617. - _Robert G. Wilson v_, Jun 22 2006
%p 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
%t OldPrimeQ[n_] := Abs[n]==1 || PrimeQ[Abs[n]]; Select[Range[2000], OldPrimeQ[Numerator[BernoulliB[ # ]/# ]] &] (* _T. D. Noe_, Jun 20 2006 *)
%Y Cf. A112548, A001067.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Jun 19 2006
%E a(21) and a(22) from _T. D. Noe_, Jun 20 2006
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