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A099319 Numerators of an approximation of Riemann to pi(n). 2

%I #8 Apr 02 2023 11:56:22

%S 0,1,3,9,3,7,4,14,61,16,35,19,41,22,22,179,97,103,109,115,115,115,121,

%T 127,65,133,45,137,143,149,155,811,817,817,817,817,847,877,877,877,

%U 907,937,967,997,997,997,1027,1057,268,1087,1087,1087,1117,1147,1147,1147,1147

%N Numerators of an approximation of Riemann to pi(n).

%C Edwards, p. 22, calls this J(n).

%D J. C. Lagarias and A. M. Odlyzko, Computing pi(x): an analytic method, J. Algorithms, 8 (1987), 173-191.

%D H. M. Edwards, Riemann's Zeta Function, Academic Press, NY, 1974.

%H T. D. Noe, <a href="/A099319/b099319.txt">Table of n, a(n) for n=1..10000</a>

%F See Maple code.

%e 0, 1/2, 3/2, 9/4, 3, 7/2, 4, 14/3, 61/12, 16/3, 35/6, 19/3,... = A099319/A099320.

%p f:=proc(n) local i,m,p,t1,t2; t1:=0; for i from 1 to n do p:=ithprime(i); if p > n then break; fi; for m from 1 to n do if p^m > n then break; fi; if n = p^m then t2:=1/(2*m) else t2:=1/m; fi; t1:=t1+t2; od; od; t1; end;

%t f[n_] := Module[{i, m, p, t1, t2}, t1 = 0; For[i = 1, i <= n, i++, p = Prime[i]; If[p > n, Break[]]; For[m = 1, m <= n, m++, If[p^m > n, Break[]]; If[n == p^m, t2 = 1/(2m), t2 = 1/m]; t1 = t1 + t2]]; t1];

%t Table[f[n] // Numerator, {n, 1, 100}] (* _Jean-Fran├žois Alcover_, Apr 02 2023, after Maple code _)

%Y Cf. A099320

%K nonn,frac

%O 1,3

%A _N. J. A. Sloane_, Nov 17 2004

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