A078435 Number of composites <= n^2.

1, 2, 5, 10, 16, 25, 34, 46, 59, 75, 91, 110, 130, 152, 177, 202, 228, 258, 289, 322, 356, 392, 430, 471, 511, 554, 600, 647, 695, 746, 799, 852, 908, 965, 1025, 1086, 1150, 1216, 1281, 1349, 1418, 1490, 1566, 1641, 1719, 1797, 1880, 1962, 2044, 2133, 2223

Offset: 1

Author

John E. Lenz (jel5010(AT)yahoo.com), Dec 30 2002

Keywords

• nonn

Examples

			a(3)=5 because the only composites <= 9 are 1, 4, 6, 8 and 9.
		

Programs

Maple

NumComposites := proc(N::posint) local count, i:count := 0:for i from 1 to N do if not isprime(i) then count := count + 1 fi:od: count;end:seq(NumComposites(k^2), k=1..51); # Zerinvary Lajos, May 26 2008
A038107 := proc(n) numtheory[pi]( n^2) ; end: A078435 := proc(n) n^2-A038107(n) ; end: seq(A078435(n),n=1..100) ; # R. J. Mathar, Jun 22 2009

Mathematica

a[n_] := n^2 - PrimePi[n^2];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Oct 20 2024, after R. J. Mathar *)

Formula

a(n) = n^2 - A038107(n). - R. J. Mathar, Jun 22 2009