A051227 Numbers m such that the Bernoulli number B_{2*m} has denominator 42.

3, 57, 93, 129, 177, 201, 213, 237, 291, 327, 381, 417, 447, 471, 489, 501, 579, 591, 597, 633, 669, 681, 687, 807, 921, 951, 1011, 1047, 1059, 1083, 1137, 1149, 1167, 1203, 1227, 1263, 1299, 1317, 1347, 1371, 1389, 1437, 1461, 1497, 1563, 1569

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) = A051228(n)/2. - Petros Hadjicostas, Jun 06 2020

Mathematica

Select[Range[1600], Denominator[BernoulliB[2#]]==42&] (* Harvey P. Dale, Nov 24 2011 *)

Prog

(Perl) @p=(2, 3, 5, 7); @c=(4); $p=7; for($n=6; $n<=3126; $n+=6){while($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)=denominator(bernfrac(2*n))==42 \\ Charles R Greathouse IV, Feb 07 2017

Crossrefs

Cf. A045979, A051222, A051225, A051226, A051228, A051229, A051230.

Sequence in context: A350336 A344690 A203483 * A122548 A078728 A032696

Adjacent sequences: A051224 A051225 A051226 * A051228 A051229 A051230

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