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

%I

%S 1,3,4,5,18,28,16,18,8,11,30,2,21,15,16,119,21,19,80,168,44,23,72,75,

%T 117,81,252,145,150,341,88,363,374,77,66,148,2,39,480,533,273,602,616,

%U 35,644,15,40,35,750,85,260,848,864,440,896,912,464,1003,1020,366,279,126,96,585

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

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

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

%p A000720 := proc(n) numtheory[pi](n) ; end:

%p A161961 := proc(n) A000720(n^2)/n/A000720(n) ; denom(%) ; end: seq(A161961(n),n=2..120) ; # _R. J. Mathar_, Oct 05 2009

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

%Y Cf. A161960, A000720.

%K nonn,frac,less

%O 2,2

%A _Daniel Tisdale_, Jun 22 2009

%E Keyword:frac added by _R. J. Mathar_, Jun 30 2009

%E Definition corrected and sequence extended by _R. J. Mathar_, Oct 05 2009

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Last modified May 28 15:55 EDT 2020. Contains 334684 sequences. (Running on oeis4.)