A200721 Product of two nonconsecutive primes p and q that divides the sum of primes between p and q, exclusively.

26, 1133, 20309, 51159, 3246905, 28673661, 5201685791

Offset: 1

Author

Manuel Valdivia, Nov 21 2011

Keywords

• nonn

Comments

Prime p is approximately q/((2*log(q)-1)*k), for k = 1, 1, 3, 307, 5041, 102378,..(quotients).

a(8) > 2*10^10. 3235398421447 is also a term. - Donovan Johnson, Nov 23 2011

Examples

			51159 = 3*17053, (5+ ... +17047)/51159 = 307.
		

Crossrefs

Cf. A055514, A055233, A086447, A086448, A001358.

Programs

Mathematica

ss[n_] := Module[{f = Transpose[FactorInteger[n]], p, q, s}, If[f[[2]] == {1, 1}, {p, q} = PrimePi[f[[1]]]; s = Total[Table[Prime[i], {i, p + 1, q - 1}]]; s != 0 && Mod[s, n] == 0, False]]; Select[Range[2, 21000], ss] (* T. D. Noe, Nov 21 2011 *)

Extensions

a(7) from Donovan Johnson, Nov 23 2011