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 A099319 Numerators of an approximation of Riemann to pi(n). 2
 0, 1, 3, 9, 3, 7, 4, 14, 61, 16, 35, 19, 41, 22, 22, 179, 97, 103, 109, 115, 115, 115, 121, 127, 65, 133, 45, 137, 143, 149, 155, 811, 817, 817, 817, 817, 847, 877, 877, 877, 907, 937, 967, 997, 997, 997, 1027, 1057, 268, 1087, 1087, 1087, 1117, 1147, 1147, 1147, 1147 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Edwards, p. 22, calls this J(n). REFERENCES J. C. Lagarias and A. M. Odlyzko, Computing pi(x): an analytic method, J. Algorithms, 8 (1987), 173-191. H. M. Edwards, Riemann's Zeta Function, Academic Press, NY, 1974. LINKS T. D. Noe, Table of n, a(n) for n=1..10000 FORMULA See Maple code. EXAMPLE 0, 1/2, 3/2, 9/4, 3, 7/2, 4, 14/3, 61/12, 16/3, 35/6, 19/3,... = A099319/A099320. MAPLE 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; MATHEMATICA 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]; Table[f[n] // Numerator, {n, 1, 100}] (* Jean-François Alcover, Apr 02 2023, after Maple code _) CROSSREFS Cf. A099320 Sequence in context: A224233 A021258 A200607 * A231828 A268580 A179802 Adjacent sequences: A099316 A099317 A099318 * A099320 A099321 A099322 KEYWORD nonn,frac AUTHOR N. J. A. Sloane, Nov 17 2004 STATUS approved

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Last modified June 12 14:48 EDT 2024. Contains 373331 sequences. (Running on oeis4.)