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A073700 a(1) = 1, a(n) = Floor[(Sum of composite numbers up to n)/(Sum of primes up to n)]. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,10

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.

LINKS

Table of n, a(n) for n=1..105.

EXAMPLE

a(10) = Floor[ {4+6+8+9+10}/{2+3+5+7)] =2.

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 *)

CROSSREFS

Sequence in context: A204897 A262618 A107577 * A226957 A108775 A300826

Adjacent sequences:  A073697 A073698 A073699 * A073701 A073702 A073703

KEYWORD

nonn

AUTHOR

Amarnath Murthy, Aug 12 2002

EXTENSIONS

More terms from Sascha Kurz, Aug 15 2002

STATUS

approved

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Last modified October 21 20:44 EDT 2019. Contains 328315 sequences. (Running on oeis4.)