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A295597 Numbers k such that Bernoulli number B_{k} has denominator 4501770.

%I A295597 #15 May 06 2018 11:02:21
%S A295597 96,20256,42144,56352,62112,70368,84576,105312,119904,146208,155616,
%T A295597 156192,165408,167136,168864,183648,187296,200352,200544,204576,
%U A295597 217824,221664,228192,234336,240288,252768,255072,255264,258144,262176,263904,266592,274272,304224,306336
%N A295597 Numbers k such that Bernoulli number B_{k} has denominator 4501770.
%C A295597 4501770 = 2*3*5*7*13*17*97.
%C A295597 All terms are multiples of a(1) = 96.
%C A295597 For these numbers numerator(B_{k}) mod denominator(B_{k}) = 3051091.
%H A295597 Seiichi Manyama, <a href="/A295597/b295597.txt">Table of n, a(n) for n = 1..1000</a>
%e A295597 Bernoulli B_{96} is
%e A295597 -211600449597266513097597728109824233673043954389060234150638733420050668349987 259/4501770 hence 96 is in the sequence.
%p A295597 with(numtheory): P:=proc(q, h) local n;  for n from 2 by 2 to q do
%p A295597 if denom(bernoulli(n))=h then print(n); fi; od; end: P(10^6, 4501770);
%p A295597 # Alternative: # according to Robert Israel code in A282773
%p A295597 with(numtheory): filter:= n ->
%p A295597 select(isprime, map(`+`, divisors(n), 1)) = {2, 3, 5, 7, 13, 17, 97}:
%p A295597 select(filter, [seq(i, i=1..10^5)]);
%t A295597 96*Flatten[Position[BernoulliB[Range[96,31*10^4,96]],_?(Denominator[ #] == 4501770&)]] (* The program takes a long time to run *) (* _Harvey P. Dale_, May 06 2018 *)
%Y A295597 Cf. A045979, A051222, A051225, A051226, A051227, A051228, A051229, A051230, A119456, A119480, A249134, A255684, A271634, A271635, A272138, A272139, A272140, A272183, A272184, A272185, A272186, A272369.
%K A295597 nonn,easy
%O A295597 1,1
%A A295597 _Paolo P. Lava_, Nov 24 2017