%I #13 Mar 12 2026 02:02:47

%S 100,1700,7100,16700,22300,25700,28300,31300,31700,33100,35300,37900,

%T 38300,38900,39700,44900,45700,47900,52100,56900,58700,60700,66100,

%U 75100,75700,78700,79700,83900,85700,85900,88100,90700,96700,99100

%N Numbers k such that Bernoulli number B_{k} has denominator 33330.

%C 33330= 2*3*5*11*101.

%C All terms are multiples of a(1) = 100.

%C For these numbers numerator(B_{k}) mod denominator(B_{k}) = 28859.

%H Seiichi Manyama, <a href="/A295589/b295589.txt">Table of n, a(n) for n = 1..1000</a>

%e Bernoulli B_{100} is

%e -945980378191221252952274330694937218727028415330669361333856962043113954151972 47711/33330, hence 100 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, 33330);

%p # Alternative: according to Robert Israel code in A282773

%p with(numtheory): filter:= n ->

%p select(isprime, map(`+`, divisors(n), 1)) = {2, 3, 5, 11, 101}:

%p select(filter, [seq(i, i=1..10^5)]);

%t Select[Range[100,100000,100],Denominator[BernoulliB[#]]==33330&] (* _Harvey P. Dale_, Aug 05 2022 *)

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

%K nonn,easy

%O 1,1

%A _Paolo P. Lava_, Nov 24 2017