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%I #29 Feb 07 2023 17:21:29
%S 1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,-1,0,0,0,-1,0,0,0,0,1,0,0,-1,0,0,0,
%T 0,1,0,0,0,1,0,0,-1,0,0,0,-1,0,0,0,0,0,0,0,0,0,1,1,0,0,-1,0,0,0,0,1,0,
%U 0,0,0,0,0,-1,-1,-1,0,0,0,-1,0,0,0,-1,-1,0,0,0,0,-1,0,0,0,0,0,1,1,0,0,0,1,0
%N Nearest integer to R(n) - pi(n), where R(x) is the Riemann prime counting function.
%C The Riemann prime counting function R(n) = Sum_{prime powers p^k <= n} 1/k = A096624(n)/A096625(n). - _N. J. A. Sloane_, Feb 07 2023
%H Harry J. Smith, <a href="/A052434/b052434.txt">Table of n, a(n) for n = 2..10000</a>
%H H. J. Smith, <a href="http://harry-j-smith-memorial.com/download.html#XPCalc">XPCalc - Extra Precision Floating-Point Calculator</a> [Broken link]
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RiemannPrimeCountingFunction.html">Riemann Prime Counting Function</a>
%e a(13) = 0 because R(13) = 5.504 and pi(13) = 6.
%o (XPCalc) a=Round(Ri(n)-Pi(n)) - _Harry J. Smith_, Dec 31 2008
%Y Cf. A052435, A096624, A096625.
%K sign
%O 2,108
%A _Eric W. Weisstein_
%E Corrected 6 terms, a(2), a(7), a(10), a(13), a(20) and a(48). Each was made 1 larger. Also gave an example for a(13) and a program for computing a(n). - _Harry J. Smith_, Dec 31 2008
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