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

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• easy

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.

Crossrefs

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

Programs

Mathematica

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

PARI

is(n)=denominator(bernfrac(2*n))==42 \\ Charles R Greathouse IV, Feb 07 2017

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"

Formula

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

Extensions

More terms and Perl program from Hugo van der Sanden

Name edited by Petros Hadjicostas, Jun 06 2020