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

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

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proposed

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proposed

a(n) = round((Product(Prime(k),_{k=1,..n} prime(k))/Factorialfactorial(n)).

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

Cf. A000142, A002110.

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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

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

Table[Round[Product[Prime[k], {k, 1, n}]/n!], {n, 1, 50}] (* G. C. Greubel, Oct 25 2017 *)

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

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

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

easy,nonn,new

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

1,1

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

Weisstein, Eric W. <a href="http://mathworld.wolfram.com/PrimeProducts.html">Prime Products</a>

a(n) = round(Product(Prime(k),k=1,n)/Factorial(n))

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

Cf. A002110.

easy,nonn

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

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