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A051227
Numbers m such that the Bernoulli number B_{2*m} has denominator 42.
32
3, 57, 93, 129, 177, 201, 213, 237, 291, 327, 381, 417, 447, 471, 489, 501, 579, 591, 597, 633, 669, 681, 687, 807, 921, 951, 1011, 1047, 1059, 1083, 1137, 1149, 1167, 1203, 1227, 1263, 1299, 1317, 1347, 1371, 1389, 1437, 1461, 1497, 1563, 1569
OFFSET
1,1
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.
G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, Th. 118.
H. Rademacher, Topics in Analytic Number Theory, Springer, 1973, Chap. 1.
FORMULA
a(n) = A051228(n)/2. - Petros Hadjicostas, Jun 06 2020
MATHEMATICA
Select[Range[1600], Denominator[BernoulliB[2#]]==42&] (* Harvey P. Dale, Nov 24 2011 *)
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/2, ", "if!grep$n%$_==0, @c; }print"\n"
(PARI) is(n)=denominator(bernfrac(2*n))==42 \\ Charles R Greathouse IV, Feb 07 2017
KEYWORD
nonn,nice,easy
EXTENSIONS
More terms and Perl program from Hugo van der Sanden
Name edited by Petros Hadjicostas, Jun 06 2020
STATUS
approved