A295594 Numbers k such that Bernoulli number B_{k} has denominator 272118.

90, 14670, 24210, 35010, 40410, 41670, 44910, 46890, 55530, 57870, 60570, 60930, 82710, 83610, 87030, 89730, 98370, 101070, 104670, 106830, 109530, 111330, 113310, 114930, 117090, 117270, 117630, 123570, 128610, 138870, 150030, 152730, 160470, 175590, 178110, 179730

Offset: 1

Author

Paolo P. Lava, Nov 24 2017

Keywords

• nonn
• easy

Comments

272118 = 2*3*7*11*19*31.

All terms are multiples of a(1) = 90.

For these numbers numerator(B_{k}) mod denominator(B_{k}) = 230759.

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, 272118);
# Alternative: # according to Robert Israel code in A282773
with(numtheory): filter:= n ->
select(isprime, map(`+`, divisors(n), 1)) = {2, 3, 7, 11, 19, 31}:
select(filter, [seq(i, i=1..10^5)]);

Formula

272118 = 2*3*7*11*19*31.

Bernoulli B_{90} is

1179057279021082799884123351249215083775254949669647116231545215727922535/ 272118 hence 90 is in the sequence.