A051229 - OEIS

A051229

Numbers m such that the Bernoulli number B_{2*m} has denominator 66.

5, 25, 85, 185, 235, 295, 305, 335, 355, 365, 395, 425, 505, 535, 635, 685, 695, 745, 815, 835, 925, 985, 995, 1115, 1135, 1145, 1285, 1315, 1345, 1385, 1415, 1445, 1475, 1525, 1535, 1555, 1565, 1585, 1655, 1675, 1735, 1765

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

From the von Staudt-Clausen theorem, denominator(B_{2*m}) = product of primes p such that (p-1)|2*m.

REFERENCES

B. C. Berndt, Ramanujan's Notebooks Part IV, Springer-Verlag, see p. 75.

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

Wikipedia, Von Staudt-Clausen theorem.

Index entries for sequences related to Bernoulli numbers.

FORMULA

a(n) = 5*A119456(n). - G. C. Greubel, Jun 06 2020

EXAMPLE

The numbers m = 5, 25 belong to the list because B_10 = 5/66 and B_50 = 495057205241079648212477525/66. - Petros Hadjicostas, Jun 06 2020

MATHEMATICA

Select[Range[2000], Denominator[BernoulliB[2 #]]==66&] (* Harvey P. Dale, Mar 11 2012 *)

PROG

(PARI) is(n)=denominator(bernfrac(2*n))==66 \\ Charles R Greathouse IV, Feb 06 2017

(Sage) [n for n in (1..2000) if denominator(bernoulli(2*n))==66 ] # G. C. Greubel, Jun 06 2020

CROSSREFS

Cf. A045979, A051222, A051225, A051226, A051227, A051228.

Equals A051230/2.

Sequence in context: A131537 A250555 A147122 * A058919 A018212 A181477

Adjacent sequences: A051226 A051227 A051228 * A051230 A051231 A051232

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Michael Somos

Name edited by Petros Hadjicostas, Jun 06 2020

STATUS

approved