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

1,5

Comments

Essentially the same as A065890.

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

Links

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

Formula

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

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

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A000277 A003664 A065890 * A373226 A213730 A191172

Adjacent sequences: A162174 A162175 A162176 * A162178 A162179 A162180

Keyword

nonn,easy

Author

Jaroslav Krizek, Jun 27 2009

Extensions

Edited and extended by Klaus Brockhaus, Sep 09 2009

Status

approved