A122093 Product of the first n 4-almost primes, divided by product of the first n primes, rounded down.

8, 64, 460, 2633, 12926, 55682, 196527, 837826, 3059886, 9285173, 26956956, 72856639, 184807084, 541527736, 1520886410, 3873955950, 8929796766, 20494615529, 45883467602, 98229395430, 209914872426, 488915652233, 1113313955086, 2451792530303, 5004689907217

Offset

1,1

Comments

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)?

Probably it can be easily proved that a(n) = 0 for n >= 802. - Giovanni Resta, Jun 13 2016

Links

Giovanni Resta, Table of n, a(n) for n = 1..1000

Formula

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))).

Example

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.

Mathematica

q = Select[Range[1000], PrimeOmega[#] == 4 &]; m = 1; Table[ Floor[ m *= q[[i]]/ Prime[i]], {i, Length@ q}] (* Giovanni Resta, Jun 13 2016 *)

Crossrefs

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

Sequence in context: A213296 A223564 A146885 * A267231 A267470 A227591

Adjacent sequences: A122090 A122091 A122092 * A122094 A122095 A122096

Keyword

easy,nonn

Author

Jonathan Vos Post, Oct 17 2006

Extensions

a(11)-a(25) from Giovanni Resta, Jun 13 2016

Status

approved