A053622 - OEIS

%I #12 Sep 08 2022 08:45:00

%S 2,1,1,0,0,0,0,0,0,0,0,-1,-1,0,0,-1,-1,-2,-1,-1,-1,-2,-1,-1,-1,-1,-1,

%T -1,-1,-2,-2,-2,-1,-1,-1,-2,-2,-1,-1,-2,-2,-3,-2,-2,-2,-3,-3,-2,-2,-2,

%U -2,-3,-2,-2,-2,-2,-2,-3,-2,-3,-3,-3,-3,-2,-2,-3,-3,-3,-3,-3,-3

%N a(n) = round( n/log(n) - pi(n) ).

%H G. C. Greubel, <a href="/A053622/b053622.txt">Table of n, a(n) for n = 2..1000</a>

%H C. K. Caldwell, <a href="http://www.utm.edu/research/primes/howmany.shtml">How Many Primes Are There?</a>

%F a(n) = A050499(n) - A000720(n).

%t Table[Round[n/Log[n] - PrimePi[n]], {n,2,80}] (* _G. C. Greubel_, Apr 20 2017 *)

%o (PARI) vector(80, n, n++; round(n/log(n) - primepi(n)) ) \\ _G. C. Greubel_, May 17 2019

%o (Magma) [Round(n/Log(n) - #PrimesUpTo(n)): n in [2..80]]; // _G. C. Greubel_, May 17 2019

%o (Sage) [round(n/log(n) - prime_pi(n)) for n in (2..80)] # _G. C. Greubel_, May 17 2019

%Y Cf. A000720, A050499, A052434, A052435.

%K sign

%O 2,1

%A _Henry Bottomley_, Mar 21 2000