A132635 Number of primes, 0's, and 1's in [0, n^2).

0, 1, 4, 6, 8, 11, 13, 17, 20, 24, 27, 32, 36, 41, 46, 50, 56, 63, 68, 74, 80, 87, 94, 101, 107, 116, 124, 131, 139, 148, 156, 164, 174, 183, 193, 202, 212, 221, 230, 242, 253, 265, 276, 285, 297, 308, 321, 331, 344, 359, 369, 380, 395, 411, 423, 436, 447, 459, 476

Offset: 0

Author

Roger L. Bagula and Gary W. Adamson, Aug 26 2008

Keywords

• nonn
• easy

Comments

Number of p-adic cyclotomic type levels in A_n-1 or SU(n).

Examples

			SU(5) at n^2-1=24 is exactly inside SU(9) at n^2-1=80.
		

Programs

Mathematica

Table[Sum[If[m == 0 || m == 1, 1, If[PrimeQ[m], 1, 0]], {m, 0,n^2 - 1}], {n, 0, 30}]

PARI

a(n)=if(n<2,n,primepi(n^2)+2) \\ Charles R Greathouse IV, Nov 07 2011

Formula

a(n) = pi(n^2) + 2 = A038107(n) + 2, n > 1. [Charles R Greathouse IV, Nov 07 2011]