A122019 - OEIS

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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 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,1`
	COMMENTS	`Note that this is nonmonotonic. What is the asymptotic value of the ratio A112141(n)/A002110(n)?`
	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.`
	CROSSREFS	`Cf. A000040, A001358, A002110, A112141, A123389.` `Sequence in context: A102988 A080137 A102933 * A190279 A186325 A033627` `Adjacent sequences: A122016 A122017 A122018 * A122020 A122021 A122022`
	KEYWORD	`easy,nonn`
	AUTHOR	`Jonathan Vos Post (jvospost3(AT)gmail.com), Oct 14 2006`

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Last modified February 17 16:49 EST 2012. Contains 206058 sequences.