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A123389 Ratio of each term of the primorial function to the corresponding term of the factorial function (rounded to nearest integer). 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 21 19:31 EDT 2019. Contains 323444 sequences. (Running on oeis4.)