1,1

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)?

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))).

a(1) = floor(16/2) = floor(8) = 8.

a(2) = floor((16*24)/(2*3)) = floor(384/6) = floor(64) = 64.

a(3) = floor(13824/30) = floor(460.8) = 460.

a(4) = floor(552960/210) = floor(2633.14286) = 2633.

Cf. A000040, A002110, A014613, A114426, A122019, A122032.

Sequence in context: A086114 A117219 A045825 this_sequence A127426 A126629 A125498

Adjacent sequences: A122090 A122091 A122092 this_sequence A122094 A122095 A122096

easy,nonn

Jonathan Vos Post (jvospost2(AT)yahoo.com), Oct 17 2006