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

%I A295587 #19 Jul 29 2025 17:50:10
%S A295587 40,6680,7880,8920,9080,10280,12520,12680,14120,15320,15560,18280,
%T A295587 20840,21640,22760,23480,25720,26440,28040,30040,30280,31880,33080,
%U A295587 33560,34520,35240,35480,36280,38680,39640,42040,43880,44360,46120,46520,46840,47240,47720,48520
%N A295587 Numbers k such that Bernoulli number B_{k} has denominator 13530.
%C A295587 13530 = 2*3*5*11*41.
%C A295587 All terms are multiples of a(1) = 40.
%C A295587 For these numbers numerator(B_{k}) mod denominator(B_{k}) = 11519.
%H A295587 Seiichi Manyama, <a href="/A295587/b295587.txt">Table of n, a(n) for n = 1..1000</a>
%e A295587 Bernoulli B_{40} is -261082718496449122051/13530, hence 40 is in the sequence.
%p A295587 with(numtheory): P:=proc(q, h) local n;  for n from 2 by 2 to q do
%p A295587 if denom(bernoulli(n))=h then print(n); fi; od; end: P(10^6,13530);
%p A295587 # Alternative: # according to Robert Israel code in A282773
%p A295587 with(numtheory): filter:= n ->
%p A295587 select(isprime, map(`+`, divisors(n), 1)) = {2, 3, 5, 11, 41}:
%p A295587 select(filter, [seq(i, i=1..10^5)]);
%t A295587 Select[Range[50000],Denominator[BernoulliB[#]]==13530&] (* _Harvey P. Dale_, Jul 29 2025 *)
%Y A295587 Cf. A045979, A051222, A051225, A051226, A051227, A051228, A051229, A051230, A119456, A119480, A249134, A255684, A271634, A271635, A272138, A272139, A272140, A272183, A272184, A272185, A272186, A272369.
%K A295587 nonn,easy
%O A295587 1,1
%A A295587 _Paolo P. Lava_, Nov 24 2017