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%I A282773 #13 Mar 08 2017 02:29:23
%S A282773 82,574,1066,1394,3034,3362,3854,4838,5494,5822,6478,7462,7954,8282,
%T A282773 8774,8938,10414,11234,12218,12382,12874,13694,15826,16154,17302,
%U A282773 18614,18778,21074,21238,21566,22058,22222,22714,23206,23534,23698,25174,25502,25994
%N A282773 Numbers n such that Bernoulli number B_{n} has denominator 498.
%C A282773 498 = 2 * 3 * 83.
%C A282773 All terms are multiples of a(1) = 82.
%C A282773 For these numbers numerator(B_{n}) mod denominator(B_{n}) = 77.
%C A282773 n such that 82 | n but there are no primes p other than 2, 3, 83 such that p-1 | n. - _Robert Israel_, Mar 07 2017
%H A282773 Robert Israel, <a href="/A282773/b282773.txt">Table of n, a(n) for n = 1..10000</a>
%H A282773 Wikipedia, <a href="https://en.wikipedia.org/wiki/Von_Staudt%E2%80%93Clausen_theorem">Von Staudt-Clausen theorem</a>
%e A282773 Bernoulli B_{82} is 1677014149185145836823154509786269900207736027570253414881613/498, hence 82 is in the sequence.
%p A282773 with(numtheory): P:=proc(q,h) local n;  for n from 2 by 2 to q do
%p A282773 if denom(bernoulli(n))=h then print(n); fi; od; end: P(10^6,498);
%p A282773 # Alternative:
%p A282773 filter:= n ->
%p A282773   select(isprime,map(`+`,numtheory:-divisors(n),1)) = {2,3,83}:
%p A282773 select(filter, [seq(i,i=82..10^5,82)]); # _Robert Israel_, Mar 07 2017
%t A282773 Select[82 Range[360], Denominator@ BernoulliB@ # == 498 &] (* _Michael De Vlieger_, Mar 07 2017 *)
%Y A282773 Cf. A045979, A051222, A051225, A051226, A051227, A051228, A051229, A051230, A119456, A119480, A249134, A255684, A271634, A271635, A272138, A272139, A272140, A272183, A272184, A272185, A272186, A272369.
%Y A282773 Cf. A002445.
%K A282773 nonn
%O A282773 1,1
%A A282773 _Paolo P. Lava_, Mar 07 2017
%E A282773 More terms from _Michael De Vlieger_, Mar 07 2017

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