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Search: id:A000146
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| A000146 |
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From von Staudt-Clausen representation of Bernoulli numbers: a(n) = Bernoulli(2n) + Sum_{(p-1)|2n} 1/p.
(Formerly M1717 N0680)
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+0
7
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| 1, 1, 1, 1, 1, 1, 2, -6, 56, -528, 6193, -86579, 1425518, -27298230, 601580875, -15116315766, 429614643062, -13711655205087, 488332318973594, -19296579341940067, 841693047573682616, -40338071854059455412
(list; graph; listen)
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OFFSET
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1,7
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COMMENT
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The von Staudt-Clausen theorem states that this number is always an integer.
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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).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, Th. 118.
Knuth, D. E.; Buckholtz, Thomas J. Computation of tangent, Euler and Bernoulli numbers. Math. Comp. 21 1967 663-688.
H. Rademacher, Topics in Analytic Number Theory, Springer, 1973, Section 5.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..100
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Index entries for sequences related to Bernoulli numbers.
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PROGRAM
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(PARI) a(n)=if(n<1, 0, sumdiv(2*n, d, isprime(d+1)/(d+1))+bernfrac(2*n))
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CROSSREFS
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Cf. also A002882, A003245, A127187, A127188.
Sequence in context: A153450 A084123 A074023 this_sequence A014070 A132525 A074167
Adjacent sequences: A000143 A000144 A000145 this_sequence A000147 A000148 A000149
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KEYWORD
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sign,nice,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Signs courtesy of xpolakis(AT)hol.gr (Antreas P. Hatzipolakis). More terms from Michael Somos
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