cp's OEIS Frontend

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

%I A120632 #17 Mar 03 2022 11:29:45
%S A120632 2,4,8,11,18,22,29,33,40,51,54,64,72,76,84,94,104,109,120,127,132,142,
%T A120632 150,161,174,181,186,194,199,207,230,238,248,252,270,275,285,297,305,
%U A120632 317,327,331,349,353,361,365,386,407,415,419,426,438,442,460,471,482
%N A120632 Number of numbers >1 up to 2*prime(n) which are divisible by primes up to prime(n).
%C A120632 The first prime(n+1)-2 numbers >1 are divisible by primes up to prime(n).
%C A120632 Complement of A137624; A137621(a(n))=A000040(n); A137621(a(n)+1)=A100484(n). - _Reinhard Zumkeller_, Jan 30 2008
%H A120632 Robert Israel, <a href="/A120632/b120632.txt">Table of n, a(n) for n = 1..10000</a>
%F A120632 a(n) = A120633(n) + A040976(n+1) = A076274(n) - A070046(n).
%e A120632 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 A120632 f:= proc(n) local p;
%p A120632    p:= ithprime(n); 2*p - numtheory:-pi(2*p)+n-1
%p A120632 end proc:
%p A120632 map(f, [$1..100]); # _Robert Israel_, Mar 02 2022
%o A120632 (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 A120632 Cf. A000040, A100484, A137621, A137624.
%Y A120632 Cf. A120633, A040976, A076274, A070046.
%K A120632 nonn
%O A120632 1,1
%A A120632 _Lekraj Beedassy_, Jun 21 2006