A123389 Ratio of each term of the primorial function to the corresponding term of the factorial function (rounded to nearest integer).

2, 3, 5, 9, 19, 42, 101, 241, 615, 1783, 5024, 15492, 48860, 150069, 470216, 1557591, 5405759, 18319515, 64600395, 229331403, 797199638, 2862671427, 10330509932, 38308974332, 148638820408, 577404648509, 2202691807275, 8417429406373, 31637924320505, 119169514940569

Offset: 1

Author

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

Keywords

• easy
• nonn

Comments

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

Examples

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

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Prime Products

Crossrefs

Cf. A000142, A002110.

Programs

Mathematica

Table[Round[Product[Prime[k], {k, 1, n}]/n!], {n, 1, 50}] (* G. C. Greubel, Oct 25 2017 *)
With[{nn=30},Round[#[[1]]/#[[2]]]&/@Thread[{FoldList[Times,Prime[ Range[ nn]]],Range[nn]!}]] (* Harvey P. Dale, Apr 06 2019 *)

PARI

for(n=1,50, print1(round(prod(k=1,n, prime(k))/n!), ", ")) \\ G. C. Greubel, Oct 25 2017

Formula

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

Extensions

Terms a(18) onward added by G. C. Greubel, Oct 25 2017