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A272383 Numbers n such that Bernoulli number B_{n} has denominator 3318.

%I A272383 #16 May 02 2016 17:38:13
%S A272383 78,1014,2418,3354,7566,8502,10842,11622,12246,12714,13026,15054,
%T A272383 15366,15522,16458,17394,23946,26286,27222,27534,29562,29874,30342,
%U A272383 31434,31902,33774,34242,35646,36114,40794,42198,43602,44538,47814,48126,48282,49218,50154,52494,55302,57174,57642,59046,59982
%N A272383 Numbers n such that Bernoulli number B_{n} has denominator 3318.
%C A272383 3318 = 2 * 3 * 7 * 79.
%C A272383 All terms are multiples of a(1) = 78.
%C A272383 For these numbers numerator(B_{n}) mod denominator(B_{n}) = 37.
%H A272383 Chai Wah Wu, <a href="/A272383/b272383.txt">Table of n, a(n) for n = 1..10000</a>
%e A272383 Bernoulli B_{78} is 414846365575400828295179035549542073492199375372400483487/3318, hence 78 is in the sequence.
%p A272383 with(numtheory): P:=proc(q,h) local n;  for n from 2 by 2 to q do
%p A272383 if denom(bernoulli(n))=h then print(n); fi; od; end: P(10^6,3318);
%t A272383 Select[78 Range@ 800, Denominator@ BernoulliB@ # == 3318 &] (* _Michael De Vlieger_, Apr 28 2016 *)
%o A272383 (PARI) lista(nn) = for(n=1, nn, if(denominator(bernfrac(n)) == 3318, print1(n, ", "))); \\ _Altug Alkan_, Apr 28 2016
%o A272383 (Python)
%o A272383 from sympy import divisors, isprime
%o A272383 A272383_list = []
%o A272383 for i in range(78, 10**6, 78):
%o A272383     for d in divisors(i):
%o A272383         if d not in (1,2,6,78) and isprime(d+1):
%o A272383             break
%o A272383     else:
%o A272383         A272383_list.append(i) # _Chai Wah Wu_, May 02 2016
%Y A272383 Cf. A045979, A051222, A051225, A051226, A051227, A051228, A051229, A051230, A119456, A119480, A249134, A255684, A271634, A271635, A272138, A272139, A272140, A272183, A272184, A272185, A272186.
%K A272383 nonn,easy
%O A272383 1,1
%A A272383 _Paolo P. Lava_, Apr 28 2016
%E A272383 a(9)-a(22) from _Altug Alkan_, Apr 28 2016
%E A272383 More terms from _Michael De Vlieger_, Apr 28 2016