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A051225 Bernoulli number B_{2n} has denominator 30. 39
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

From the von Staudt-Clausen theorem, denominator(B_2n) = product of primes p such that (p-1)|2n.

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

Index entries for sequences related to Bernoulli numbers.

MATHEMATICA

Cases[Range[760], n_ /; Denominator[BernoulliB[2*n]] == 30] (* Jean-Fran├žois 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-A051230.

Sequence in context: A200980 A178811 A099433 * A103625 A006989 A236399

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

STATUS

approved

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Last modified February 19 12:09 EST 2019. Contains 320310 sequences. (Running on oeis4.)