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

1,1

Comments

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

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Prime Products

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A000142, A002110.

Sequence in context: A058770 A049910 A077643 * A113984 A110542 A101542

Adjacent sequences: A123386 A123387 A123388 * A123390 A123391 A123392

Keyword

easy,nonn

Author

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

Extensions

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

Status

approved