login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A123389 Ratio of each term of the primorial function to the corresponding term of the factorial function (rounded to nearest integer). 3

%I #9 Apr 06 2019 13:59:22

%S 2,3,5,9,19,42,101,241,615,1783,5024,15492,48860,150069,470216,

%T 1557591,5405759,18319515,64600395,229331403,797199638,2862671427,

%U 10330509932,38308974332,148638820408,577404648509,2202691807275,8417429406373,31637924320505,119169514940569

%N Ratio of each term of the primorial function to the corresponding term of the factorial function (rounded to nearest integer).

%C Shows how the primorial function grows in comparison to the factorial function.

%H G. C. Greubel, <a href="/A123389/b123389.txt">Table of n, a(n) for n = 1..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeProducts.html">Prime Products</a>

%F a(n) = round((Product_{k=1..n} prime(k))/factorial(n)).

%e a(5)= round((2*3*5*7*11)/(1*2*3*4*5)) = round(2310/120) = round(19.25) = 19.

%t Table[Round[Product[Prime[k], {k, 1, n}]/n!], {n, 1, 50}] (* _G. C. Greubel_, Oct 25 2017 *)

%t With[{nn=30},Round[#[[1]]/#[[2]]]&/@Thread[{FoldList[Times,Prime[ Range[ nn]]],Range[nn]!}]] (* _Harvey P. Dale_, Apr 06 2019 *)

%o (PARI) for(n=1,50, print1(round(prod(k=1,n, prime(k))/n!), ", ")) \\ _G. C. Greubel_, Oct 25 2017

%Y Cf. A000142, A002110.

%K easy,nonn

%O 1,1

%A Mitch Cervinka (puritan(AT)toast.net), Oct 13 2006

%E Terms a(18) onward added by _G. C. Greubel_, Oct 25 2017

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 08:02 EDT 2024. Contains 371236 sequences. (Running on oeis4.)