A120632 Number of numbers >1 up to 2*prime(n) which are divisible by primes up to prime(n).

2, 4, 8, 11, 18, 22, 29, 33, 40, 51, 54, 64, 72, 76, 84, 94, 104, 109, 120, 127, 132, 142, 150, 161, 174, 181, 186, 194, 199, 207, 230, 238, 248, 252, 270, 275, 285, 297, 305, 317, 327, 331, 349, 353, 361, 365, 386, 407, 415, 419, 426, 438, 442, 460, 471, 482

Offset: 1

Author

Lekraj Beedassy, Jun 21 2006

Keywords

• nonn

Comments

The first prime(n+1)-2 numbers >1 are divisible by primes up to prime(n).

Complement of A137624; A137621(a(n))=A000040(n); A137621(a(n)+1)=A100484(n). - Reinhard Zumkeller, Jan 30 2008

Examples

			a(4)=11 because exactly 11 numbers between 2 and 2*prime(4)=2*7=14, namely: 2,3,4,5,6,7,8,9,10,12,14 are divisible by the first four primes 2,3,5,7.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A100484, A137621, A137624.

Cf. A120633, A040976, A076274, A070046.

Programs

Maple

f:= proc(n) local p;
   p:= ithprime(n); 2*p - numtheory:-pi(2*p)+n-1
end proc:
map(f, [$1..100]); # Robert Israel, Mar 02 2022

PARI

a(n) = {nb = 0; for (i = 2, 2*prime(n), for (ip = 1, n, if ( !(i % prime(ip)), nb++; break;););); nb;} \\ Michel Marcus, Oct 26 2013

Formula

a(n) = A120633(n) + A040976(n+1) = A076274(n) - A070046(n).