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.
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
KEYWORD
nonn,frac
AUTHOR
N. J. A. Sloane, Nov 17 2004
STATUS
approved