cp's OEIS Frontend

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

%I A073700 #15 Aug 21 2024 01:56:07
%S A073700 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,
%T A073700 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,
%U A073700 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
%N A073700 a(1) = 1, a(n) = Floor[(Sum of composite numbers up to n)/(Sum of primes up to n)].
%C A073700 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.
%C A073700 Note 1 is neither composite nor prime.
%F A073700 a(n) = floor(A101256(n)/A034387(n)). - _Jason Yuen_, Aug 20 2024
%e A073700 a(10) = floor((4+6+8+9+10)/(2+3+5+7)) = floor(37/17) = 2.
%p A073700 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);
%t A073700 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 *)
%t A073700 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 *)
%Y A073700 Cf. A101256, A034387.
%K A073700 nonn
%O A073700 1,10
%A A073700 _Amarnath Murthy_, Aug 12 2002
%E A073700 More terms from _Sascha Kurz_, Aug 15 2002