A161893 Denominators of S(n) = Sum_{j=2..n} (pi((j+1)^2) - pi(j^2))/(pi((j+1)^2)*pi(j^2)) where pi(k) = A000720(k).

4, 3, 18, 22, 30, 9, 11, 50, 15, 17, 78, 44, 48, 27, 122, 33, 72, 39, 170, 92, 198, 210, 57, 61, 258, 274, 73, 77, 81, 172, 362, 382, 200, 105, 438, 228, 240, 502, 526, 137, 566, 590, 153, 638, 658, 171, 714, 734, 189, 786, 818, 842, 217, 890, 914, 237, 974, 1006, 1038, 532, 1098, 564, 289, 297

Offset

2,1

Comments

The sum converges rapidly to 1/2; S(100) = 0.4992..., S(500) = 0.49995....

Links

Table of n, a(n) for n=2..65.

Example

First few fractions are 1/4, 1/3, 7/18, 9/22, 13/30, 4/9, 5/11, 23/50, 7/15, ...

Prog

(PARI) a(n) = denominator(sum(k=2, n, (primepi((k+1)^2) - primepi(k^2))/(primepi((k+1)^2)*primepi(k^2)))); \\ Michel Marcus, Aug 15 2022

Crossrefs

Cf. A000720 (pi), A161892 (numerators).

Cf. A161621.

Sequence in context: A302851 A373946 A276083 * A192773 A183231 A241358

Adjacent sequences: A161890 A161891 A161892 * A161894 A161895 A161896

Keyword

nonn,frac,less

Author

Daniel Tisdale, Jun 21 2009

Extensions

Offset 2 and more terms from Michel Marcus, Aug 15 2022

Status

approved