A073882 Number of primes between n and n^2.

0, 2, 3, 4, 7, 8, 12, 14, 18, 21, 26, 29, 34, 38, 42, 48, 55, 59, 65, 70, 77, 84, 91, 96, 105, 113, 120, 128, 137, 144, 152, 161, 170, 180, 189, 199, 208, 216, 228, 239, 251, 261, 270, 281, 292, 305, 315, 327, 342, 352, 363, 378, 394, 405, 418, 429, 441, 458, 471

Offset: 1

Author

Amarnath Murthy, Aug 16 2002

Keywords

• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000720, A010051, A038107, A117490.

Programs

Mathematica

Table[c=PrimePi[n^2]-PrimePi[n];If[PrimeQ[n],c+1,c],{n,59}] (* James C. McMahon, Jan 12 2025 *)

PARI

a(n)=sum(k=n,n^2,isprime(k))

Formula

a(n) = A038107(n) - A000720(n) + A010051(n). - Reinhard Zumkeller, May 20 2010

a(n) = Sum_{k=n..n^2} A010051(k) = A117490(n) + A010051(n). - Reinhard Zumkeller, May 20 2010

Extensions

Corrected and extended by Benoit Cloitre, Aug 20 2002