A051225 Numbers m such that the Bernoulli number B_{2*m} has denominator 30.

2, 4, 34, 38, 62, 76, 94, 118, 122, 124, 142, 188, 202, 206, 214, 218, 236, 244, 274, 298, 302, 314, 334, 362, 394, 412, 422, 436, 446, 454, 458, 482, 514, 526, 538, 542, 566, 578, 604, 622, 626, 628, 634, 662, 668, 674, 694, 698, 706, 722, 724, 734, 758

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.

G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, Th. 118.

H. Rademacher, Topics in Analytic Number Theory, Springer, 1973, Chap. 1.

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) = A051226(n)/2. - Petros Hadjicostas, Jun 06 2020

Example

The numbers m = 2, 4, 34 are in the list because B_4 = B_8 = -1/30 and B_68 = -78773130858718728141909149208474606244347001/30. - Petros Hadjicostas, Jun 06 2020

Mathematica

Cases[Range[760], n_ /; Denominator[BernoulliB[2*n]] == 30] (* Jean-François Alcover, Mar 23 2011 *)

Prog

(Perl) @p=(2, 3, 5); $p=5; for($n=4; $n<=1516; $n+=4){while($p<$n+1){$p+=2; next if grep$p%$_==0, @p; push@p, $p; push@c, $p-1; }print$n/2, ", "if!grep$n%$_==0, @c; }print"\n"
(PARI) is(n)=fordiv(n, d, if(isprime(2*d+1) && d>2, return(0))); n%2==0 \\ Charles R Greathouse IV, Jun 21 2017

Crossrefs

Cf. A045979, A051222, A051226, A051227, A051228, A051229, A051230.

Sequence in context: A178811 A099433 A373344 * A306582 A103625 A006989

Adjacent sequences: A051222 A051223 A051224 * A051226 A051227 A051228

Keyword

nonn,nice,easy

Author

N. J. A. Sloane

Extensions

More terms and Perl program from Hugo van der Sanden

Name edited by Petros Hadjicostas, Jun 06 2020

Status

approved