A200721 - OEIS

%I #15 Jul 18 2019 05:09:17

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

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

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

%C a(8) > 2*10^10. 3235398421447 is also a term. - _Donovan Johnson_, Nov 23 2011

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

%t 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 *)

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

%K nonn

%O 1,1

%A _Manuel Valdivia_, Nov 21 2011

%E a(7) from _Donovan Johnson_, Nov 23 2011