A073700 a(1) = 1, a(n) = Floor[(Sum of composite numbers up to n)/(Sum of primes up to n)].

1, 0, 0, 0, 0, 1, 0, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 2, 2, 3, 3, 3, 3, 3, 3, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 2, 2, 3, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3

Offset: 1

Author

Amarnath Murthy, Aug 12 2002

Keywords

• nonn

Comments

Though the sequence is not monotonically increasing the average value increases and a derived sequence could be the smallest value of k for which a(k) = n.

Note 1 is neither composite nor prime.

Examples

			a(10) = floor((4+6+8+9+10)/(2+3+5+7)) = floor(37/17) = 2.
		

Crossrefs

Cf. A101256, A034387.

Programs

Maple

a := 0:b := 0:for i from 2 to 300 do if isprime(i) then a := a+i: else b := b+i:fi: c[i] := floor(b/a):od:c[1] := 1:seq(c[j],j=1..300);

Mathematica

Module[{nn=110,pr,comp},pr=Prime[Range[PrimePi[nn]]];comp=Complement[Range[ 2,nn], pr]; Join[{1}, Table[Floor[Total[Select[comp,#<=n&]]/Total[Select[pr,#<=n&]]],{n,2,nn}]]] (* Harvey P. Dale, Feb 22 2013 *)
Join[{1}, Table[t1 = Select[x = Range[n], PrimeQ]; Floor[Divide @@ Plus @@@ {Rest[Complement[x, t1]], t1}], {n, 2, 105}]] (* Jayanta Basu, Jul 07 2013 *)

Formula

a(n) = floor(A101256(n)/A034387(n)). - Jason Yuen, Aug 20 2024

Extensions

More terms from Sascha Kurz, Aug 15 2002