%I A002815 M2523 N0996
%S A002815 0,1,3,6,9,13,17,22,27,32,37,43,49,56,63,70,77,85,93,102,111,120,129,139,
%T A002815 149,159,169,179,189,200,211,223,235,247,259,271,283,296,309,322,335,
%U A002815 349,363,378,393,408,423,439,455,471
%N A002815 a(n) = n + Sum_{k=1..n} pi(k), where pi() = A000720.
%C A002815 The g.f. (-1+z**7+z**8-z**4-z**2-z)/(z+1)/(z**2-z+1)/(z**2+z+1)/(z-1)**3 
               conjectured by S. Plouffe in his 1992 dissertation is wrong.
%D A002815 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002815 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002815 H. Brocard, Reply to Query 1421, Nombres premiers dans une suite de differences, 
               L'Interm\'{e}diaire des Math\'{e}maticiens, 7 (1900), 135-137.
%H A002815 T. D. Noe, <a href="b002815.txt">Table of n, a(n) for n=0..1000</a>
%H A002815 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
               Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
               a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A002815 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
               1031 Generating Functions and Conjectures</a>, Universit\'{e} du 
               Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%t A002815 Table[n + Sum[PrimePi[k], {k, 1, n}], {n, 0, 50}]
%Y A002815 Cf. A000720.
%Y A002815 Sequence in context: A061781 A123753 A124288 this_sequence A109512 A025205 
               A024190
%Y A002815 Adjacent sequences: A002812 A002813 A002814 this_sequence A002816 A002817 
               A002818
%K A002815 nonn,nice,easy
%O A002815 0,3
%A A002815 N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com), 
               Mira Bernstein (mira(AT)math.berkeley.edu)