|
Search: id:A099319
|
|
|
| A099319 |
|
Numerators of an approximation of Riemann to pi(n). |
|
+0
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; listen)
|
|
|
OFFSET
|
1,3
|
|
|
COMMENT
|
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.
|
|
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;
|
|
CROSSREFS
|
Cf. A099320
Sequence in context: A074959 A010632 A021258 this_sequence A010707 A097665 A083996
Adjacent sequences: A099316 A099317 A099318 this_sequence A099320 A099321 A099322
|
|
KEYWORD
|
nonn,frac
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com), Nov 17 2004
|
|
|
Search completed in 0.002 seconds
|
