A282512 Denominator of the sum of the reciprocals of the first n nonprimes.

1, 4, 12, 24, 72, 360, 360, 2520, 504, 1008, 336, 1680, 1680, 18480, 18480, 92400, 1201200, 10810800, 10810800, 10810800, 21621600, 21621600, 367567200, 52509600, 52509600, 997682400, 997682400, 997682400, 6983776800, 6983776800, 6983776800, 160626866400, 160626866400, 1124388064800, 1124388064800

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
		

Links

• Robert Israel, Table of n, a(n) for n = 1..3954

Crossrefs

Cf. A018252 (nonprime numbers), A282511 (numerators).

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

Maple

NP:= remove(isprime, [$1..100]):
S:= ListTools:-PartialSums(map(t -> 1/t, NP)):
map(denom, S); # Robert Israel, May 01 2017

Mathematica

With[{nn=50}, Denominator@Accumulate[1/Complement[Range@nn, Prime@Range@PrimePi@nn]]] (* Vincenzo Librandi, May 02 2017 *)

Extensions

Corrected by Robert Israel, May 01 2017