A282511 Numerator of the sum of the reciprocals of the first n nonprimes.

1, 5, 17, 37, 119, 631, 661, 4807, 995, 2053, 703, 3599, 3679, 41309, 42079, 214091, 2829383, 25864847, 26250947, 26611307, 53898289, 54553489, 938220113, 135531719, 136990319, 2629070861, 2654652461, 2679594521, 18923442047, 19082164247, 19237359287

Offset: 1

Author

Ralf Steiner, Feb 17 2017

Keywords

• nonn
• frac

Examples

			The first few fractions are 1, 5/4, 17/12, 37/24, 119/72, 631/360, 661/360, 4807/2520, 995/504, 2053/
1008, 703/336, 3599/1680, ... - _N. J. A. Sloane_, Dec 15 2017
		

Crossrefs

Cf. A018252 (nonprime numbers), A282512 (denominators).

The following fractions are all related to each other: Sum 1/n: A001008/A002805, Sum 1/prime(n): A024451/A002110 and A106830/A034386, Sum 1/nonprime(n): A282511/A282512, Sum 1/composite(n): A250133/A296358.

Programs

Mathematica

With[{nn = 45}, Numerator@ Accumulate[1/Complement[Range@ nn, Prime@ Range@ PrimePi@ nn]]] (* Michael De Vlieger, Feb 18 2017 *)

PARI

a018252(n) = if(n==1, 1, my(i=1); forcomposite(c=1, , i++; if(i==n, return(c))))
a(n) = numerator(sum(k=1, n, 1/a018252(k))) \\ Felix Fröhlich, Feb 17 2017

Extensions

More terms from Felix Fröhlich, Feb 17 2017