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A051227
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Numbers m such that the Bernoulli number B_{2*m} has denominator 42.
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32
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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
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OFFSET
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1,1
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COMMENTS
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From the von Staudt-Clausen theorem, denominator(B_{2*m}) = product of primes p such that (p-1)|2*m.
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REFERENCES
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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.
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LINKS
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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.
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FORMULA
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a(n) = A051228(n)/2. - Petros Hadjicostas, Jun 06 2020
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MATHEMATICA
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Select[Range[1600], Denominator[BernoulliB[2#]]==42&] (* Harvey P. Dale, Nov 24 2011 *)
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PROG
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(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
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CROSSREFS
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Cf. A045979, A051222, A051225, A051226, A051228, A051229, A051230.
Sequence in context: A070731 A132489 A203483 * A122548 A078728 A032696
Adjacent sequences: A051224 A051225 A051226 * A051228 A051229 A051230
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KEYWORD
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nonn,nice,easy
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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More terms and Perl program from Hugo van der Sanden
Name edited by Petros Hadjicostas, Jun 06 2020
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STATUS
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approved
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