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A272139 Numbers n such that Bernoulli number B_{n} has denominator 1806.

%I A272139 #30 Jun 01 2019 11:31:35
%S A272139 42,294,798,1806,2058,2814,2982,4074,4578,5334,5586,6594,6846,8106,
%T A272139 8274,8358,9366,9534,12642,12894,13314,14154,14658,15162,17178,18186,
%U A272139 19194,20118,20454,21882,21966,22722,22974,23982,25914,26502,27006,28266,28518,29778
%N A272139 Numbers n such that Bernoulli number B_{n} has denominator 1806.
%C A272139 1806 = 2 * 3 * 7 * 43.
%C A272139 All terms are multiple of a(1) = 42.
%C A272139 For these numbers numerator(B_{n}) mod denominator(B_{n}) = 1.
%C A272139 In 2005, B. C. Kellner proved E. W. Weisstein's conjecture that denom(B_n) = n only if n = 1806.
%H A272139 Seiichi Manyama, <a href="/A272139/b272139.txt">Table of n, a(n) for n = 1..1000</a>
%e A272139 Bernoulli B_{42} is 1520097643918070802691/1806, hence 42 is in the sequence.
%p A272139 with(numtheory): P:=proc(q,h) local n;  for n from 2 by 2 to q do
%p A272139 if denom(bernoulli(n))=h then print(n); fi; od; end: P(10^6,1806);
%t A272139 Select[Range[0, 1000], Denominator[BernoulliB[#]] == 1806 &] (* _Robert Price_, Apr 21 2016 *)
%t A272139 Select[Range[42,30000,42],Denominator[BernoulliB[#]]==1806&] (* _Harvey P. Dale_, Jun 01 2019 *)
%o A272139 (PARI) lista(nn) = for(n=1, nn, if(denominator(bernfrac(n)) == 1806, print1(n, ", "))); \\ _Altug Alkan_, Apr 22 2016
%Y A272139 Cf. A045979, A051222, A051225, A051226, A051227, A051228, A051229, A051230, A119456, A119480, A249134, A255684, A271634, A271635, A272138,  A272140, A272183, A272184, A272185, A272186.
%K A272139 nonn
%O A272139 1,1
%A A272139 _Paolo P. Lava_, Apr 21 2016
%E A272139 More terms from _Altug Alkan_, Apr 22 2016