A053622 a(n) = round( n/log(n) - pi(n) ).

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, -1, -1, -2, -2, -2, -1, -1, -1, -2, -2, -1, -1, -2, -2, -3, -2, -2, -2, -3, -3, -2, -2, -2, -2, -3, -2, -2, -2, -2, -2, -3, -2, -3, -3, -3, -3, -2, -2, -3, -3, -3, -3, -3, -3

Offset: 2

Author

Henry Bottomley, Mar 21 2000

Keywords

• sign

Links

• G. C. Greubel, Table of n, a(n) for n = 2..1000
• C. K. Caldwell, How Many Primes Are There?

Crossrefs

Cf. A000720, A050499, A052434, A052435.

Programs

Magma

[Round(n/Log(n) - #PrimesUpTo(n)): n in [2..80]]; // G. C. Greubel, May 17 2019

Mathematica

Table[Round[n/Log[n] - PrimePi[n]], {n,2,80}] (* G. C. Greubel, Apr 20 2017 *)

PARI

vector(80, n, n++; round(n/log(n) - primepi(n)) ) \\ G. C. Greubel, May 17 2019

Sage

[round(n/log(n) - prime_pi(n)) for n in (2..80)] # G. C. Greubel, May 17 2019

Formula

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