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
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
KEYWORD
nonn,nice,easy
AUTHOR
EXTENSIONS
More terms and Perl program from Hugo van der Sanden
Name edited by Petros Hadjicostas, Jun 06 2020
STATUS
approved