cp's OEIS Frontend

A036234 Number of primes <= n, if 1 is counted as a prime.

%I A036234 #50 Dec 12 2015 02:46:41
%S A036234 1,2,3,3,4,4,5,5,5,5,6,6,7,7,7,7,8,8,9,9,9,9,10,10,10,10,10,10,11,11,
%T A036234 12,12,12,12,12,12,13,13,13,13,14,14,15,15,15,15,16,16,16,16,16,16,17,
%U A036234 17,17,17,17,17,18,18,19,19,19,19,19,19,20,20,20,20
%N A036234 Number of primes <= n, if 1 is counted as a prime.
%C A036234 This sequence is the largest nondecreasing sequence a(n) such that a(Prime(n)-1) = n. - _Tanya Khovanova_, Jun 20 2007
%C A036234 Partial sums of A080339. - _Jaroslav Krizek_, Mar 23 2009
%C A036234 Let G(n) be the graph whose vertices represent integers 1 through n, and where vertices a and b are adjacent iff gcd(a,b)>1. Then a(n) is the independence number of G(n). - _Aaron Dunigan AtLee_, May 23 2009
%C A036234 a(1)=1; a(n)= max[A061395(n), A061395(n-1)]. - _Jacques ALARDET_, Dec 28 2011
%C A036234 It appears that a(n) is the minimal index i for which binomial(k*prime(i), prime(i)) mod prime(i) = k. For example, binomial(11*prime(n), prime(n)) mod prime(n) produces the sequence 1,2,1,4,0,11,11,11,11 and a(11)=6. It also appears that binomial(k*prime(a(n)-1), prime(a(n)-1)) mod prime(a(n)-1) = 0 iff k is prime. - _Gary Detlefs_, Aug 05 2013
%C A036234 a(n) is the number of noncomposite numbers <= n. The noncomposite number are in A008578. - _Omar E. Pol_, Aug 31 2013
%C A036234 Number of distinct terms in n-th row of the triangle in A080786. - _Reinhard Zumkeller_, Sep 10 2013
%H A036234 Reinhard Zumkeller, <a href="/A036234/b036234.txt">Table of n, a(n) for n = 1..10000</a>
%F A036234 a(n) = A000720(n) + 1. - _Jaroslav Krizek_, Mar 23 2009
%p A036234 A036234 := proc(n)
%p A036234     if n = 1 then
%p A036234         1;
%p A036234     else
%p A036234         1+numtheory[pi](n) ;
%p A036234     end if;
%p A036234 end proc: # _R. J. Mathar_, Jan 28 2014
%t A036234 Table[PrimePi[n] + 1, {n, 100}] (* _Tanya Khovanova_, Jun 20 2007 *)
%o A036234 (Haskell)
%o A036234 a036234 = (+ 1) . a000720  -- _Reinhard Zumkeller_, Sep 10 2013
%o A036234 (PARI) a(n)=primepi(n)+1 \\ _Charles R Greathouse IV_, Apr 29 2015
%Y A036234 Cf. A000720, A080339, A147693.
%K A036234 nonn
%O A036234 1,2
%A A036234 _N. J. A. Sloane_