A295770 Numbers k such that Bernoulli number B_{k} has denominator 4686.

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

Offset: 1

Author

Paolo P. Lava, Nov 27 2017

Keywords

• nonn
• easy

Comments

4686 = 2*3*11*71.

All terms are multiples of a(1) = 70.

For these numbers numerator(B_{k}) mod denominator(B_{k}) = 289.

Examples

			Bernoulli B_{70} is 1505381347333367003803076567377857208511438160235/4686, hence 70 is in the sequence.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A045979, A051222, A051225, A051226, A051227, A051228, A051229, A051230, A119456, A119480, A249134, A255684, A271634, A271635, A272138, A272139, A272140, A272183, A272184, A272185, A272186, A272369.

Programs

Maple

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)]);

Mathematica

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 *)

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