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Numbers k such that Bernoulli number B_k has denominator 2730.
29

%I #50 Mar 17 2024 02:14:02

%S 12,24,1308,1884,2004,2364,2532,2724,3804,4008,4044,4188,4236,4668,

%T 5052,5064,5268,5388,5484,6252,6492,6564,6756,6852,7044,7188,7356,

%U 7404,7608,7764,8124,8412,8472,8796,9084,9228,9852,9876,9924

%N Numbers k such that Bernoulli number B_k has denominator 2730.

%C 2730 = 2 * 3 * 5 * 7 * 13.

%H Charles R Greathouse IV, <a href="/A249134/b249134.txt">Table of n, a(n) for n = 1..10000</a>

%e BernoulliB(12) is -691/2730, hence 12 is in the sequence.

%t Reap[For[n = 0, n <= 10^4, n = n+12, If[Denominator[BernoulliB[n]] == 2730, Print[n]; Sow[n]]]][[2, 1]]

%t Select[Table[n, {n, 2, 10000}], Denominator@BernoulliB[#]==2730 &] (* _Vincenzo Librandi_, Apr 02 2015 *)

%o (PARI) is(n)=denominator(bernfrac(n))==2730 \\ _Charles R Greathouse IV_, Oct 22 2014

%o (PARI) is(n)=if(n%12 || n%16==0 || n%9==0, return(0)); forprime(p=5,107, if(n%p==0, return(0))); fordiv(n,d, if(isprime(d+1) && d>13, return(0))); 1 \\ _Charles R Greathouse IV_, Oct 22 2014

%Y Cf. A000367, A002445, A006954, A027642, A027760, A027762, A051222, A051225-A051230, A245056, A271634, A271635, A272138, A272139, A272140, A272183, A272184, A272185, A272186.

%K nonn

%O 1,1

%A _Jean-François Alcover_ and _Paul Curtz_, Oct 22 2014