A282773 - OEIS

%I #13 Mar 08 2017 02:29:23

%S 82,574,1066,1394,3034,3362,3854,4838,5494,5822,6478,7462,7954,8282,

%T 8774,8938,10414,11234,12218,12382,12874,13694,15826,16154,17302,

%U 18614,18778,21074,21238,21566,22058,22222,22714,23206,23534,23698,25174,25502,25994

%N Numbers n such that Bernoulli number B_{n} has denominator 498.

%C 498 = 2 * 3 * 83.

%C All terms are multiples of a(1) = 82.

%C For these numbers numerator(B_{n}) mod denominator(B_{n}) = 77.

%C 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 Robert Israel, <a href="/A282773/b282773.txt">Table of n, a(n) for n = 1..10000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Von_Staudt%E2%80%93Clausen_theorem">Von Staudt-Clausen theorem</a>

%e Bernoulli B_{82} is 1677014149185145836823154509786269900207736027570253414881613/498, hence 82 is in the sequence.

%p with(numtheory): P:=proc(q,h) local n;  for n from 2 by 2 to q do

%p if denom(bernoulli(n))=h then print(n); fi; od; end: P(10^6,498);

%p # Alternative:

%p filter:= n ->

%p   select(isprime,map(`+`,numtheory:-divisors(n),1)) = {2,3,83}:

%p select(filter, [seq(i,i=82..10^5,82)]); # _Robert Israel_, Mar 07 2017

%t Select[82 Range[360], Denominator@ BernoulliB@ # == 498 &] (* _Michael De Vlieger_, Mar 07 2017 *)

%Y Cf. A045979, A051222, A051225, A051226, A051227, A051228, A051229, A051230, A119456, A119480, A249134, A255684, A271634, A271635, A272138, A272139, A272140, A272183, A272184, A272185, A272186, A272369.

%Y Cf. A002445.

%K nonn

%O 1,1

%A _Paolo P. Lava_, Mar 07 2017

%E More terms from _Michael De Vlieger_, Mar 07 2017