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A295770
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Numbers k such that Bernoulli number B_{k} has denominator 4686.
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1
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70, 350, 4970, 5110, 7070, 8890, 9590, 9730, 13790, 15610, 15890, 16030, 17990, 18410, 19810, 21770, 22190, 23170, 24290, 25550, 26530, 26810, 27230, 28070, 30310, 32270, 32690, 33530, 34930, 36470, 38990, 39830, 40390, 43190, 44450, 45010, 48650, 49070, 49630, 51730
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OFFSET
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1,1
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COMMENTS
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4686 = 2*3*11*71.
All terms are multiples of a(1) = 70.
For these numbers numerator(B_{k}) mod denominator(B_{k}) = 289.
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LINKS
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EXAMPLE
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Bernoulli B_{70} is 1505381347333367003803076567377857208511438160235/4686, hence 70 is in the sequence.
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MAPLE
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with(numtheory): P:=proc(q, h) local n; for n from 2 by 2 to q do
if denom(bernoulli(n))=h then print(n); fi; od; end: P(10^6, 4686);
# Alternative: # according to Robert Israel code in A282773
with(numtheory): filter:= n ->
select(isprime, map(`+`, divisors(n), 1)) = {2, 3, 11, 71}:
select(filter, [seq(i, i=1..10^5)]);
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MATHEMATICA
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70 Position[Array[Denominator@ BernoulliB[70 #] &, 10^3], 4686][[All, 1]] (* Michael De Vlieger, Nov 27 2017 *)
Select[70*Range[750], Denominator[BernoulliB[#]]==4686&] (* Harvey P. Dale, Nov 23 2023 *)
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PROG
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(PARI) isok(n) = denominator(bernfrac(n)) == 4686; \\ Michel Marcus, Nov 27 2017
(PARI) lista(nn) = forstep(n=70, nn, 70, if(denominator(bernfrac(n)) == 4686, print1(n, ", "))) \\ Iain Fox, Nov 27 2017
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CROSSREFS
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Cf. A045979, A051222, A051225, A051226, A051227, A051228, A051229, A051230, A119456, A119480, A249134, A255684, A271634, A271635, A272138, A272139, A272140, A272183, A272184, A272185, A272186, A272369.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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