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%I #25 Jun 06 2020 17:51:19
%S 3,57,93,129,177,201,213,237,291,327,381,417,447,471,489,501,579,591,
%T 597,633,669,681,687,807,921,951,1011,1047,1059,1083,1137,1149,1167,
%U 1203,1227,1263,1299,1317,1347,1371,1389,1437,1461,1497,1563,1569
%N Numbers m such that the Bernoulli number B_{2*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.
%D G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, Th. 118.
%D H. Rademacher, Topics in Analytic Number Theory, Springer, 1973, Chap. 1.
%H T. D. Noe, <a href="/A051227/b051227.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) = A051228(n)/2. - _Petros Hadjicostas_, Jun 06 2020
%t Select[Range[1600],Denominator[BernoulliB[2#]]==42&] (* _Harvey P. Dale_, Nov 24 2011 *)
%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$n/2,","if!grep$n%$_==0,@c; }print"\n"
%o (PARI) is(n)=denominator(bernfrac(2*n))==42 \\ _Charles R Greathouse IV_, Feb 07 2017
%Y Cf. A045979, A051222, A051225, A051226, A051228, 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
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