A126147 a(n) = floor((Product_{k=1..n-1} prime(k))/prime(n)).

0, 0, 1, 4, 19, 177, 1766, 26868, 421725, 7692857, 208699781, 5420553787, 180993613044, 7075587523888, 278356624078085, 11601694011103611, 552358618257458385, 31520661477937912115, 1750572856110551805720

Offset: 1

Author

Leroy Quet, Mar 07 2007

Keywords

• nonn

Comments

Every distinct prime dividing ((Product_{k=1..n-1} prime(k)) (mod prime(n))) also divides a(n).

Let Pn(n) = A002110(n) denote the primorial function. The number of natural numbers < Pn(n) that have prime(n+1) as a prime factor is equal to a(n). For example 19 numbers < Pn(4) = 210 have 11 as a prime factor. - Jamie Morken, Sep 18 2018

Links

• Muniru A Asiru, Table of n, a(n) for n = 1..185

Crossrefs

Cf. A062347, A002110.

Programs

Maple

seq(floor(mul(ithprime(k),k=1..n-1)/ithprime(n)),n=1..20); # Muniru A Asiru, Sep 21 2018

Mathematica

f[n_] := Floor[ Product[ Prime@k, {k, n - 1}] / Prime@n]; Array[f, 19] (* Robert G. Wilson v, Mar 07 2007 *)

Extensions

More terms from Robert G. Wilson v, Mar 07 2007