A282773 Numbers n such that Bernoulli number B_{n} has denominator 498.

82, 574, 1066, 1394, 3034, 3362, 3854, 4838, 5494, 5822, 6478, 7462, 7954, 8282, 8774, 8938, 10414, 11234, 12218, 12382, 12874, 13694, 15826, 16154, 17302, 18614, 18778, 21074, 21238, 21566, 22058, 22222, 22714, 23206, 23534, 23698, 25174, 25502, 25994

Offset: 1

Author

Paolo P. Lava, Mar 07 2017

Keywords

• nonn

Comments

498 = 2 * 3 * 83.

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

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

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

Examples

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

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Wikipedia, Von Staudt-Clausen theorem

Crossrefs

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

Cf. A002445.

Programs

Maple

with(numtheory): P:=proc(q,h) local n;  for n from 2 by 2 to q do
if denom(bernoulli(n))=h then print(n); fi; od; end: P(10^6,498);
# Alternative:
filter:= n ->
  select(isprime,map(`+`,numtheory:-divisors(n),1)) = {2,3,83}:
select(filter, [seq(i,i=82..10^5,82)]); # Robert Israel, Mar 07 2017

Mathematica

Select[82 Range[360], Denominator@ BernoulliB@ # == 498 &] (* Michael De Vlieger, Mar 07 2017 *)

Extensions

More terms from Michael De Vlieger, Mar 07 2017