A135568 a(n) = floor( Product_{i=1..n} prime(i)/i ).

1, 2, 3, 5, 8, 19, 41, 101, 240, 614, 1782, 5024, 15492, 48859, 150069, 470216, 1557591, 5405758, 18319515, 64600395, 229331402, 797199637, 2862671427, 10330509932, 38308974332, 148638820408

Offset: 0

Author

Ctibor O. Zizka, Feb 23 2008

Keywords

• easy
• nonn

Comments

Does there exist an n such that (the product of the first n primes)/n! is an integer for n>3?

The answer to the question above is obviously no: for n>3 the denominator is a multiple of 4. - Emeric Deutsch, Mar 14 2008

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

Examples

			a(5) = floor(2*3*5*7*11/5!) = floor(2310/120) = 19.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000040, A000142, A002110.

Programs

Maple

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

Mathematica

Table[Floor[Product[Prime[i]/i, {i, n}]], {n, 0, 25}] (* G. C. Greubel, Oct 19 2016 *)

Formula

a(n) = floor(product of the first n primes/n!).

a(n) = floor( A002110(n) / A000142(n) ).

Extensions

Corrected and extended by Emeric Deutsch, Mar 14 2008