A099320 Denominators of an approximation of Riemann to pi(n).

1, 2, 2, 4, 1, 2, 1, 3, 12, 3, 6, 3, 6, 3, 3, 24, 12, 12, 12, 12, 12, 12, 12, 12, 6, 12, 4, 12, 12, 12, 12, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 15, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 5, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60

Offset

1,2

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 (2087), 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

Example

0, 1/2, 3/2, 9/4, 3, 7/2, 4, 14/3, 61/12, 16/3, 35/6, 19/3,...

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] // Denominator, {n, 1, 100}] (* Jean-François Alcover, Apr 02 2023, after Maple code in A099319 *)

Crossrefs

See A099319 for definition and program.

Sequence in context: A143485 A181633 A245204 * A206714 A230442 A034951

Adjacent sequences: A099317 A099318 A099319 * A099321 A099322 A099323

Keyword

nonn,frac

Author

N. J. A. Sloane, Nov 17 2004

Status

approved