A120632 - OEIS

%I #17 Mar 03 2022 11:29:45

%S 2,4,8,11,18,22,29,33,40,51,54,64,72,76,84,94,104,109,120,127,132,142,

%T 150,161,174,181,186,194,199,207,230,238,248,252,270,275,285,297,305,

%U 317,327,331,349,353,361,365,386,407,415,419,426,438,442,460,471,482

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

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

%C Complement of A137624; A137621(a(n))=A000040(n); A137621(a(n)+1)=A100484(n). - _Reinhard Zumkeller_, Jan 30 2008

%H Robert Israel, <a href="/A120632/b120632.txt">Table of n, a(n) for n = 1..10000</a>

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

%e 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.

%p f:= proc(n) local p;

%p    p:= ithprime(n); 2*p - numtheory:-pi(2*p)+n-1

%p end proc:

%p map(f, [$1..100]); # _Robert Israel_, Mar 02 2022

%o (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

%Y Cf. A000040, A100484, A137621, A137624.

%Y Cf. A120633, A040976, A076274, A070046.

%K nonn

%O 1,1

%A _Lekraj Beedassy_, Jun 21 2006