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Search: id:A006954
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| A006954 |
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Denominators of Bernoulli numbers B_0, B_1, B_2, B_4, B_6, ...
(Formerly M1689)
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+0
12
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| 1, 2, 6, 30, 42, 30, 66, 2730, 6, 510, 798, 330, 138, 2730, 6, 870, 14322, 510, 6, 1919190, 6, 13530, 1806, 690, 282, 46410, 66, 1590, 798, 870, 354, 56786730, 6, 510, 64722, 30, 4686, 140100870, 6, 30, 3318, 230010, 498, 3404310, 6, 61410, 272118, 1410, 6, 4501770
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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These are the denominators if you hurriedly look down a list of the nonzero Bernoulli numbers without noticing that B_1 has been included.
From the Von Staudt-Clausen theorem, denominator(B_2n) = product of primes p such that (p-1)|2n.
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 260.
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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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 260.
Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.
Index entries for sequences related to Bernoulli numbers.
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FORMULA
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E.g.f: t/(e^t - 1).
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CROSSREFS
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Cf. A000367, A002445, A027762.
Sequence in context: A095198 A126989 A128040 this_sequence A090801 A166062 A127517
Adjacent sequences: A006951 A006952 A006953 this_sequence A006955 A006956 A006957
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KEYWORD
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nonn,frac
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
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EXTENSIONS
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More terms from T. D. Noe (noe(AT)sspectra.com), Mar 31 2004
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