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A051225 Bernoulli number B_{2n} has denominator 30. 39


%S 2,4,34,38,62,76,94,118,122,124,142,188,202,206,214,218,236,244,274,

%T 298,302,314,334,362,394,412,422,436,446,454,458,482,514,526,538,542,

%U 566,578,604,622,626,628,634,662,668,674,694,698,706,722,724,734,758

%N Bernoulli number B_{2n} has denominator 30.

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

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

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

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

%H T. D. Noe, <a href="/A051225/b051225.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Be#Bernoulli">Index entries for sequences related to Bernoulli numbers.</a>

%t Cases[Range[760], n_ /; Denominator[BernoulliB[2*n]] == 30] (* _Jean-Fran├žois Alcover_, Mar 23 2011 *)

%o (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"

%o (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

%Y Cf. A045979, A051222, A051226-A051230.

%K nonn,nice,easy

%O 1,1

%A _N. J. A. Sloane_

%E More terms and Perl program from _Hugo van der Sanden_

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Last modified March 26 16:33 EDT 2019. Contains 321510 sequences. (Running on oeis4.)