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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• easy

Comments

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

Examples

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

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.

Crossrefs

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

Equals A051230/2.

Programs

Mathematica

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

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

Formula

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

Extensions

More terms from Michael Somos

Name edited by Petros Hadjicostas, Jun 06 2020