Search: id:A000146
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%I A000146 M1717 N0680
%S A000146 1,1,1,1,1,1,2,6,56,528,6193,86579,1425518,27298230,601580875,
%T A000146 15116315766,429614643062,13711655205087,488332318973594,
%U A000146 19296579341940067,841693047573682616,40338071854059455412
%V A000146 1,1,1,1,1,1,2,-6,56,-528,6193,-86579,1425518,-27298230,601580875,
%W A000146 -15116315766,429614643062,-13711655205087,488332318973594,
%X A000146 -19296579341940067,841693047573682616,-40338071854059455412
%N A000146 From von Staudt-Clausen representation of Bernoulli numbers: a(n) = Bernoulli(2n) 
               + Sum_{(p-1)|2n} 1/p.
%C A000146 The von Staudt-Clausen theorem states that this number is always an integer.
%D A000146 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000146 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000146 G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 
               5th ed., Oxford Univ. Press, 1979, Th. 118.
%D A000146 Knuth, D. E.; Buckholtz, Thomas J. Computation of tangent, Euler and 
               Bernoulli numbers. Math. Comp. 21 1967 663-688.
%D A000146 H. Rademacher, Topics in Analytic Number Theory, Springer, 1973, Section 
               5.
%H A000146 T. D. Noe, <a href="b000146.txt">Table of n, a(n) for n=1..100</a>
%H A000146 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               vonStaudt-ClausenTheorem.html">Link to a section of The World of 
               Mathematics.</a>
%H A000146 <a href="Sindx_Be.html#Bernoulli">Index entries for sequences related 
               to Bernoulli numbers.</a>
%o A000146 (PARI) a(n)=if(n<1,0,sumdiv(2*n,d, isprime(d+1)/(d+1))+bernfrac(2*n))
%Y A000146 Cf. also A002882, A003245, A127187, A127188.
%Y A000146 Sequence in context: A153450 A084123 A074023 this_sequence A014070 A132525 
               A074167
%Y A000146 Adjacent sequences: A000143 A000144 A000145 this_sequence A000147 A000148 
               A000149
%K A000146 sign,nice,easy
%O A000146 1,7
%A A000146 N. J. A. Sloane (njas(AT)research.att.com).
%E A000146 Signs courtesy of xpolakis(AT)hol.gr (Antreas P. Hatzipolakis). More 
               terms from Michael Somos

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