A051226 Numbers m such that the Bernoulli number B_m has denominator 30.

4, 8, 68, 76, 124, 152, 188, 236, 244, 248, 284, 376, 404, 412, 428, 436, 472, 488, 548, 596, 604, 628, 668, 724, 788, 824, 844, 872, 892, 908, 916, 964, 1028, 1052, 1076, 1084, 1132, 1156, 1208, 1244, 1252, 1256, 1268, 1324, 1336, 1348, 1388

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) = 2*A051225(n). - Petros Hadjicostas, Jun 06 2020

Example

The numbers m = 4, 8, 68 are in the list because B_4 = B_8 = -1/30 and B_68 = -78773130858718728141909149208474606244347001/30. - Petros Hadjicostas, Jun 06 2020

Mathematica

Select[Table[n, {n, 4, 1500, 2}], Denominator @ BernoulliB[#] == 30 &] [[1 ;; 47]] (* Jean-François Alcover, Apr 08 2011 *)

Prog

(Perl) @p=(2, 3, 5); $p=5; for($n=4; $n<=1388; $n+=4){while($p<$n+1){$p+=2; next if grep$p%$_==0, @p; push@p, $p; push@c, $p-1; }print"$n, "if!grep$n%$_==0, @c; }print"\n"
(PARI) lista(nn) = for (n=1, nn, if (denominator(bernfrac(n)) == 30, print1(n, ", "))); \\ Michel Marcus, Mar 30 2015

Crossrefs

Cf. A045979, A051222, A051225, A051227, A051228, A051229, A051230.

Sequence in context: A117636 A285634 A228930 * A013112 A274461 A206346

Adjacent sequences: A051223 A051224 A051225 * A051227 A051228 A051229

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