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

96, 20256, 42144, 56352, 62112, 70368, 84576, 105312, 119904, 146208, 155616, 156192, 165408, 167136, 168864, 183648, 187296, 200352, 200544, 204576, 217824, 221664, 228192, 234336, 240288, 252768, 255072, 255264, 258144, 262176, 263904, 266592, 274272, 304224, 306336

Offset

1,1

Comments

4501770 = 2*3*5*7*13*17*97.

All terms are multiples of a(1) = 96.

For these numbers numerator(B_{k}) mod denominator(B_{k}) = 3051091.

Links

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

Example

Bernoulli B_{96} is
-211600449597266513097597728109824233673043954389060234150638733420050668349987 259/4501770 hence 96 is in the sequence.

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, 4501770);
# Alternative: # according to Robert Israel code in A282773
with(numtheory): filter:= n ->
select(isprime, map(`+`, divisors(n), 1)) = {2, 3, 5, 7, 13, 17, 97}:
select(filter, [seq(i, i=1..10^5)]);

Mathematica

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 *)

Crossrefs

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

Sequence in context: A183418 A299950 A269208 * A203489 A208794 A276099

Adjacent sequences: A295594 A295595 A295596 * A295598 A295599 A295600

Keyword

nonn,easy

Author

Paolo P. Lava, Nov 24 2017

Status

approved