A162177 a(n) is the number of composite numbers that are smaller than A008578(n).

0, 0, 0, 1, 2, 5, 6, 9, 10, 13, 18, 19, 24, 27, 28, 31, 36, 41, 42, 47, 50, 51, 56, 59, 64, 71, 74, 75, 78, 79, 82, 95, 98, 103, 104, 113, 114, 119, 124, 127, 132, 137, 138, 147, 148, 151, 152, 163, 174, 177, 178, 181, 186, 187, 196, 201, 206, 211, 212, 217, 220, 221

Offset: 1

Author

Jaroslav Krizek, Jun 27 2009

Keywords

• nonn
• easy

Comments

Essentially the same as A065890.

a(n) = number of terms of A073169(n) less than n.

Examples

			A008578(6) = 11, and there are 5 composites smaller than 11, viz. 4, 6, 8, 9, 10, hence a(6) = 5.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A002808 (composites), A008578 (1 and the primes), A065890, A073169.

Programs

Magma

T:=[0,1] cat PrimesUpTo(300); [ T[n+1]-n: n in [1..#T-1] ]; // Klaus Brockhaus, Sep 08 2009

Mathematica

Join[{0},Module[{nn=300,cmps},cmps=Accumulate[Table[If[CompositeQ[n],1,0],{n,nn}]];Table[cmps[[p]],{p,Prime[ Range[ PrimePi[ nn]]]}]]] (* Harvey P. Dale, Nov 11 2024 *)

Formula

a(n) = A008578(n) - n = A158611(n+1) -n.

a(n) = A065890(n-1) for n > 1.

Extensions

Edited and extended by Klaus Brockhaus, Sep 09 2009