A051228 Numbers m such that the Bernoulli number B_m has denominator 42.

6, 114, 186, 258, 354, 402, 426, 474, 582, 654, 762, 834, 894, 942, 978, 1002, 1158, 1182, 1194, 1266, 1338, 1362, 1374, 1614, 1842, 1902, 2022, 2094, 2118, 2166, 2274, 2298, 2334, 2406, 2454, 2526, 2598, 2634, 2694, 2742, 2778, 2874, 2922, 2994, 3126

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.

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. A014117, A045979, A051222, A051225, A051226, A051227, A051229, A051230.

Programs

Mathematica

2*Select[Range[2000], Denominator[BernoulliB[2#]] == 42 &](* Jean-François Alcover, Nov 25 2011 *)
Position[BernoulliB[Range[3200]],?(Denominator[#]==42&)]//Flatten (* _Harvey P. Dale, Jul 02 2018 *)

PARI

is(n)=denominator(bernfrac(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"$n,"if!grep$n%$==0,@c; }print"\n"

Formula

a(n) = 2*A051227(n). - Petros Hadjicostas, Jun 06 2020

Extensions

More terms and Perl program from Hugo van der Sanden

Name edited by Petros Hadjicostas, Jun 06 2020