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

1,1

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

Links

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

Formula

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

Example

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.

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

Prog

(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

Crossrefs

Cf. A000040, A100484, A137621, A137624.

Cf. A120633, A040976, A076274, A070046.

Sequence in context: A279098 A010068 A295674 * A007295 A053439 A337501

Adjacent sequences: A120629 A120630 A120631 * A120633 A120634 A120635

Keyword

nonn

Author

Lekraj Beedassy, Jun 21 2006

Status

approved