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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
4
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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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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.
Adjacent sequences: A000143 A000144 A000145 this_sequence A000147 A000148 A000149
Sequence in context: A122593 A084123 A074023 this_sequence A014070 A132525 A074167
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KEYWORD
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sign,nice,easy
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AUTHOR
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njas
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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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