Search: id:A119766
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%I A119766
%S A119766 1,2,4,6,8,10,12,14,16,18,26,34,36,38,42,74,114,118,396,674,1870,4306,
%T A119766 22808
%N A119766 Numbers n such that numerator of Bernoulli(n)/n is (apart from sign) 
               1 or a prime.
%C A119766 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 A119766 K. Ono, Honoring a gift from Kumbakonam, Notices Amer. Math. Soc., 53 
               (2006), 640-651.
%D A119766 S. Ramanujan, Some properties of Bernoulli's numbers, J. Indian Math. 
               Soc., 3 (1911), 219-234.
%e A119766 As an example Bernoulli(20)/20= -174611/6600, but 174611=283*617. - Robert 
               G. Wilson v Jun 22 2006.
%p A119766 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 (mathar(AT)strw.leidenuniv.nl), 
               Jun 21 2006
%t A119766 OldPrimeQ[n_] := Abs[n]==1 || PrimeQ[Abs[n]]; Select[Range[2000], OldPrimeQ[Numerator[BernoulliB[ 
               # ]/# ]] &] - T. D. Noe (noe(AT)sspectra.com), Jun 20 2006
%Y A119766 Cf. A112548, A001067.
%Y A119766 Sequence in context: A118070 A152966 A066122 this_sequence A030143 A110725 
               A100800
%Y A119766 Adjacent sequences: A119763 A119764 A119765 this_sequence A119767 A119768 
               A119769
%K A119766 nonn
%O A119766 1,2
%A A119766 N. J. A. Sloane (njas(AT)research.att.com), Jun 19 2006
%E A119766 a(21) and a(22) from T. D. Noe (noe(AT)sspectra.com), Jun 20 2006

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