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%I #7 Jun 13 2016 07:23:25
%S 8,64,460,2633,12926,55682,196527,837826,3059886,9285173,26956956,
%T 72856639,184807084,541527736,1520886410,3873955950,8929796766,
%U 20494615529,45883467602,98229395430,209914872426,488915652233,1113313955086,2451792530303,5004689907217
%N Product of the first n 4-almost primes, divided by product of the first n primes, rounded down.
%C This is to 4-almost primes as A122032 is to 3-almost primes and as A122019 is to 2-almost primes (semiprimes). Note that these can nonmonotonic (look at the graphs). What is the asymptotic value of the ratio A114426(n)/A002110(n)?
%C Probably it can be easily proved that a(n) = 0 for n >= 802. - _Giovanni Resta_, Jun 13 2016
%H Giovanni Resta, <a href="/A122093/b122093.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = floor(A114426(n)/A002110(n)) = floor(Prod(i=1..n)4almostprime(i)/Prod(i=1..n)prime(i)) = floor(Prod(i=1..n)A014613(i)/Prod(i=1..n)A000040(i)) = floor(Prod(i=1..n)(A014613(i)/A000040(i))).
%e a(1) = floor(16/2) = floor(8) = 8.
%e a(2) = floor((16*24)/(2*3)) = floor(384/6) = floor(64) = 64.
%e a(3) = floor(13824/30) = floor(460.8) = 460.
%e a(4) = floor(552960/210) = floor(2633.14286) = 2633.
%t q = Select[Range[1000], PrimeOmega[#] == 4 &]; m = 1; Table[ Floor[ m *= q[[i]]/ Prime[i]], {i, Length@ q}] (* _Giovanni Resta_, Jun 13 2016 *)
%Y Cf. A000040, A002110, A014613, A114426, A122019, A122032.
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Oct 17 2006
%E a(11)-a(25) from _Giovanni Resta_, Jun 13 2016