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A122019 Product of the first n semiprimes, divided by product of the first n primes, rounded down. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 19 04:19 EDT 2019. Contains 322237 sequences. (Running on oeis4.)