%I #25 Oct 04 2020 23:32:22
%S 1,2,3,5,8,19,41,101,240,614,1782,5024,15492,48859,150069,470216,
%T 1557591,5405758,18319515,64600395,229331402,797199637,2862671427,
%U 10330509932,38308974332,148638820408
%N a(n) = floor( Product_{i=1..n} prime(i)/i ).
%C Does there exist an n such that (the product of the first n primes)/n! is an integer for n>3?
%C The answer to the question above is obviously no: for n>3 the denominator is a multiple of 4. - _Emeric Deutsch_, Mar 14 2008
%C Product_{i=1..n} (p_i/i) is the volume of the n-dimensional simplex with its n+1 vertices at (0, 0, 0, ..., 0), (p_1, 0, 0, ..., 0), (0, p_2, 0, ..., 0), (0, 0, p_3, ..., 0), ..., (0, 0, 0, ..., p_n) in Cartesian coordinates, where p_i is the i-th prime. - _Ya-Ping Lu_, Sep 21 2020
%H G. C. Greubel, <a href="/A135568/b135568.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = floor(product of the first n primes/n!).
%F a(n) = floor( A002110(n) / A000142(n) ).
%e a(5) = floor(2*3*5*7*11/5!) = floor(2310/120) = 19.
%p a:=proc(n) options operator, arrow: floor(mul(ithprime(i)/i,i=1..n)) end proc: seq(a(n),n=1..25); # _Emeric Deutsch_, Mar 14 2008
%t Table[Floor[Product[Prime[i]/i, {i, n}]], {n, 0, 25}] (* _G. C. Greubel_, Oct 19 2016 *)
%Y Cf. A000040, A000142, A002110.
%K easy,nonn
%O 0,2
%A _Ctibor O. Zizka_, Feb 23 2008
%E Corrected and extended by _Emeric Deutsch_, Mar 14 2008