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

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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..82.

Formula

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))).

Example

a(1) = floor(4/2) = floor(2) = 2.
a(2) = floor(24/6) = floor(4) = 4.
a(3) = floor(216/30) = floor(7.2) = 7.
a(4) = floor(2160/210) = floor(10.2857143) = 10.
a(5) = floor(30240/2310) = floor(13.0909090909) = 13.
a(6) = floor(453600/30030) = floor(15.1048951) = 15.
a(7) = floor(9525600/510510) = floor(18.6589881) = 18.
a(8) = floor(209563200/9699690) = floor(21.6051441) = 21.
a(9) = floor(5239080000/223092870) = floor(23.4838523) = 23.
a(10) = floor(136216080000/6469693230) = floor(21.0544882) = 21.
a(11) = floor(4495130640000/200560490130) = floor(22.4128423) = 22.
a(12) = floor(152834441760000/7420738134810) = floor(20.5955848) = 20.

Mathematica

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

Crossrefs

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

Sequence in context: A102988 A080137 A102933 * A190279 A186325 A272059

Adjacent sequences: A122016 A122017 A122018 * A122020 A122021 A122022

Keyword

easy,nonn

Author

Jonathan Vos Post, Oct 14 2006

Extensions

a(13)-a(82) from Giovanni Resta, Jun 13 2016

Status

approved