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

Author

Paolo P. Lava, Nov 24 2017

Keywords

• nonn
• easy

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.

Examples

			Bernoulli B_{96} is
-211600449597266513097597728109824233673043954389060234150638733420050668349987 259/4501770 hence 96 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, 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 *)