%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
|