1,1

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

a(n) = floor(A114425(n)/A002110(n)) = floor(Prod(i=1..n)3almostprime(i)/Prod(i=1..n)prime(i)) = floor(Prod(i=1..n)A014612(i)/Prod(i=1..n)A000040(i)) = floor(Prod(i=1..n)(A014612(i)/A000040(i))).

a(1) = floor(8/2) = floor(4) = 4.

a(2) = floor(96/6) = floor(4) = 16.

a(3) = floor(1728/30) = floor(57.6) = 57.

a(4) = floor(34560/210) = floor(164.571429) = 164.

a(5) = floor(933120/2310) = floor(403.948052) = 403.

a(6) = floor(26127360/30030) = floor(870.041958) = 870.

a(7) = floor(783820800/510510) = floor(1535.36816) = 1535.

a(8) = floor(32920473600/9699690) = floor(3393.97172) = 3393.

a(9) = floor(1448500838400/223092870) = floor(6492.81547) = 6492.

a(10) = floor(65182537728000/223092870) = floor(292176.696) = 292176.

a(11) = floor(3259126886400000/200560490130) = floor(16250.0943) = 16250.

a(12) = floor(169474598092800000/7420738134810) = floor(22837.9704) = 22837.

Cf. A000040, A014612, A002110, A112141, A123389.

Sequence in context: A057585 A097128 A006079 this_sequence A034514 A168583 A126644

Adjacent sequences: A122029 A122030 A122031 this_sequence A122033 A122034 A122035

easy,nonn

Jonathan Vos Post (jvospost3(AT)gmail.com), Oct 14 2006