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A051228 Numbers m such that the Bernoulli number B_m has denominator 42. 32
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

From the von Staudt-Clausen theorem, denominator(B_{2*m}) = product of primes p such that (p-1)|2*m.

Numerator(B_m) mod Denominator(B_m) = 1. This relation stands also for B_m with denominator equal to 1, 2, 6 and 1806 (A014117). - Paolo P. Lava, Mar 07 2017

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.

FORMULA

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

MATHEMATICA

2*Select[Range[2000], Denominator[BernoulliB[2#]] == 42 &](* Jean-Fran├žois Alcover, Nov 25 2011 *)

Position[BernoulliB[Range[3200]], _?(Denominator[#]==42&)]//Flatten (* Harvey P. Dale, Jul 02 2018 *)

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, "if!grep$n%$_==0, @c; }print"\n"

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

CROSSREFS

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

Sequence in context: A291917 A066931 A324669 * A194132 A194476 A059116

Adjacent sequences:  A051225 A051226 A051227 * A051229 A051230 A051231

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

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Last modified June 25 04:01 EDT 2021. Contains 345450 sequences. (Running on oeis4.)