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