%I #19 May 28 2016 09:21:20

%S 53,61,157,229,307,439,613,757,769,823,853,859,883,907,937,967,1009,

%T 1297,1423,1429,1447,1483,1489,1549,1597,1663,1693,1993,2083,2137,

%U 2203,2239,2389,2437,2659,2689,2707,2749,2833,2857,2953,3019,3037,3163,3187

%N Primes p such that the number of distinct prime divisors of all composite numbers between p and the next prime is 7.

%H Daria Micovic, <a href="/A075587/b075587.txt">Table of n, a(n) for n = 1..10000</a>

%t pd[n_]:=Transpose[FactorInteger[n]][[1]]; Transpose[Select[ Partition[ Prime[ Range[500]],2,1],Length[Union[Flatten[ pd/@Range[First[#]+1, Last[#]-1]]]] == 7&]][[1]] (* _Harvey P. Dale_, Jun 15 2013 *)

%t Select[Prime@ Range@ 500, Length@ Union@ Flatten@ Map[First /@ FactorInteger@ # &, Select[Range[#, NextPrime@ #], CompositeQ]] == 7 &] (* _Michael De Vlieger_, May 27 2016 *)

%Y Cf. A052297, A075581, A075580, A059960, A075583, A075584, A075585, A075586, A075588, A075589.

%K nonn

%O 1,1

%A _Amarnath Murthy_, Sep 26 2002

%E Corrected and extended by _Matthew Conroy_, Apr 30 2003

%E Name edited by _Michel Marcus_, May 28 2016