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

1,1

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

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Wikipedia, Von Staudt-Clausen theorem

Example

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

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 *)

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.

Sequence in context: A316241 A305951 A317212 * A182277 A342832 A186688

Adjacent sequences: A282770 A282771 A282772 * A282774 A282775 A282776

Keyword

nonn

Author

Paolo P. Lava, Mar 07 2017

Extensions

More terms from Michael De Vlieger, Mar 07 2017

Status

approved