%I #33 Feb 19 2024 01:57:44
%S 6,114,186,258,354,402,426,474,582,654,762,834,894,942,978,1002,1158,
%T 1182,1194,1266,1338,1362,1374,1614,1842,1902,2022,2094,2118,2166,
%U 2274,2298,2334,2406,2454,2526,2598,2634,2694,2742,2778,2874,2922,2994,3126
%N Numbers m such that the Bernoulli number B_m has denominator 42.
%C From the von Staudt-Clausen theorem, denominator(B_{2*m}) = product of primes p such that (p-1)|2*m.
%D B. C. Berndt, Ramanujan's Notebooks Part IV, Springer-Verlag, see p. 75.
%H T. D. Noe, <a href="/A051228/b051228.txt">Table of n, a(n) for n = 1..1000</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Von_Staudt%E2%80%93Clausen_theorem">Von Staudt-Clausen theorem</a>.
%H <a href="/index/Be#Bernoulli">Index entries for sequences related to Bernoulli numbers</a>.
%F a(n) = 2*A051227(n). - _Petros Hadjicostas_, Jun 06 2020
%t 2*Select[Range[2000], Denominator[BernoulliB[2#]] == 42 &](* _Jean-François Alcover_, Nov 25 2011 *)
%t Position[BernoulliB[Range[3200]],_?(Denominator[#]==42&)]//Flatten (* _Harvey P. Dale_, Jul 02 2018 *)
%o (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"
%o (PARI) is(n)=denominator(bernfrac(n))==42 \\ _Charles R Greathouse IV_, Feb 07 2017
%Y Cf. A014117, A045979, A051222, A051225, A051226, A051227, A051229, A051230.
%K nonn,nice,easy
%O 1,1
%A _N. J. A. Sloane_
%E More terms and Perl program from _Hugo van der Sanden_
%E Name edited by _Petros Hadjicostas_, Jun 06 2020