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A122019 Product of the first n semiprimes, divided by product of the first n primes, rounded down. 2

%I

%S 2,4,7,10,13,15,18,21,23,21,22,20,17,15,12,11,9,7,6,5,4,3,2,1,1,1,0,0,

%T 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,

%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0

%N Product of the first n semiprimes, divided by product of the first n primes, rounded down.

%C Note that this is nonmonotonic. What is the asymptotic value of the ratio A112141(n)/A002110(n)?

%F a(n) = floor(A112141(n)/A002110(n)) = floor(Prod(i=1..n)semiprime(i)/Prod(i=1..n)prime(i)) = floor(Prod(i=1..n)A001358(i)/Prod(i=1..n)A000040(i)) = floor(Prod(i=1..n)(A001358(i)/A000040(i))).

%e a(1) = floor(4/2) = floor(2) = 2.

%e a(2) = floor(24/6) = floor(4) = 4.

%e a(3) = floor(216/30) = floor(7.2) = 7.

%e a(4) = floor(2160/210) = floor(10.2857143) = 10.

%e a(5) = floor(30240/2310) = floor(13.0909090909) = 13.

%e a(6) = floor(453600/30030) = floor(15.1048951) = 15.

%e a(7) = floor(9525600/510510) = floor(18.6589881) = 18.

%e a(8) = floor(209563200/9699690) = floor(21.6051441) = 21.

%e a(9) = floor(5239080000/223092870) = floor(23.4838523) = 23.

%e a(10) = floor(136216080000/6469693230) = floor(21.0544882) = 21.

%e a(11) = floor(4495130640000/200560490130) = floor(22.4128423) = 22.

%e a(12) = floor(152834441760000/7420738134810) = floor(20.5955848) = 20.

%t sp = Select[Range@ 250, PrimeOmega[#] == 2 &]; m = 1; Table[ Floor[m *= sp[[i]] / Prime[i]], {i, Length@ sp}] (* _Giovanni Resta_, Jun 13 2016 *)

%Y Cf. A000040, A001358, A002110, A112141, A123389.

%K easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Oct 14 2006

%E a(13)-a(82) from _Giovanni Resta_, Jun 13 2016

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Last modified May 21 00:41 EDT 2019. Contains 323427 sequences. (Running on oeis4.)