login
a(n) is the number of composite numbers that are smaller than A008578(n).
4

%I #18 Nov 11 2024 12:27:04

%S 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,

%T 71,74,75,78,79,82,95,98,103,104,113,114,119,124,127,132,137,138,147,

%U 148,151,152,163,174,177,178,181,186,187,196,201,206,211,212,217,220,221

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

%C Essentially the same as A065890.

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

%H Harvey P. Dale, <a href="/A162177/b162177.txt">Table of n, a(n) for n = 1..1000</a>

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

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

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

%t 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 *)

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

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

%K nonn,easy

%O 1,5

%A _Jaroslav Krizek_, Jun 27 2009

%E Edited and extended by _Klaus Brockhaus_, Sep 09 2009