A295588 - OEIS

%I #18 Feb 08 2021 21:55:23

%S 30,1770,3810,4170,4470,4890,5910,5970,6810,8070,9210,10590,11370,

%T 11670,12030,12990,13470,13890,14370,14970,15630,16890,17070,17610,

%U 18510,18570,19290,19410,20190,20310,21270,22710,24810,25710,26310,27570,27870,29010,29490,29730

%N Numbers k such that Bernoulli number B_{k} has denominator 14322.

%C 14322 = 2*3*7*11*31.

%C All terms are multiples of a(1) = 30.

%C For these numbers numerator(B_{k}) mod denominator(B_{k}) = 12899.

%H Seiichi Manyama, <a href="/A295588/b295588.txt">Table of n, a(n) for n = 1..1000</a>

%e Bernoulli B_{30} is 8615841276005/14322, hence 30 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(10^6,14322);

%p # Alternative: # according to _Robert Israel_ code in A282773

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

%p select(isprime, map(`+`, divisors(n), 1)) = {2, 3, 7, 11, 31}:

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

%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