A161961 Denominator of ratio in lowest terms of pi(n^2)/(n*pi(n)), where pi(x) = A000720(x).

1, 3, 4, 5, 18, 28, 16, 18, 8, 11, 30, 2, 21, 15, 16, 119, 21, 19, 80, 168, 44, 23, 72, 75, 117, 81, 252, 145, 150, 341, 88, 363, 374, 77, 66, 148, 2, 39, 480, 533, 273, 602, 616, 35, 644, 15, 40, 35, 750, 85, 260, 848, 864, 440, 896, 912, 464, 1003, 1020, 366, 279, 126, 96, 585

Offset: 2

Author

Daniel Tisdale, Jun 22 2009

Keywords

• nonn
• frac
• less

Comments

Conjecture: S(n) = pi(n^2)/(n*pi(n)) ~ 1/2.

Examples

			The first few fractions S(n) are 1, 2/3, 3/4, 3/5, 11/18, 15/28, 9/16, 11/18, 5/8, ...
		

Crossrefs

Cf. A161960, A000720.

Programs

Maple

A000720 := proc(n) numtheory[pi](n) ; end:
A161961 := proc(n) A000720(n^2)/n/A000720(n) ; denom(%) ; end: seq(A161961(n),n=2..120) ; # R. J. Mathar, Oct 05 2009

Mathematica

Table[PrimePi[n^2]/(n*PrimePi[n]),{n,1,100}]

Extensions

Keyword:frac added by R. J. Mathar, Jun 30 2009

Definition corrected and sequence extended by R. J. Mathar, Oct 05 2009