A295587 Numbers k such that Bernoulli number B_{k} has denominator 13530.

40, 6680, 7880, 8920, 9080, 10280, 12520, 12680, 14120, 15320, 15560, 18280, 20840, 21640, 22760, 23480, 25720, 26440, 28040, 30040, 30280, 31880, 33080, 33560, 34520, 35240, 35480, 36280, 38680, 39640, 42040, 43880, 44360, 46120, 46520, 46840, 47240, 47720, 48520

Offset: 1

Author

Paolo P. Lava, Nov 24 2017

Keywords

• nonn
• easy

Comments

13530 = 2*3*5*11*41.

All terms are multiples of a(1) = 40.

For these numbers numerator(B_{k}) mod denominator(B_{k}) = 11519.

Examples

			Bernoulli B_{40} is -261082718496449122051/13530, hence 40 is in the sequence.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..1000

Crossrefs

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

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(10^6,13530);
# Alternative: # according to Robert Israel code in A282773
with(numtheory): filter:= n ->
select(isprime, map(`+`, divisors(n), 1)) = {2, 3, 5, 11, 41}:
select(filter, [seq(i, i=1..10^5)]);

Mathematica

Select[Range[50000],Denominator[BernoulliB[#]]==13530&] (* Harvey P. Dale, Jul 29 2025 *)