A075587 Primes p such that the number of distinct prime divisors of all composite numbers between p and the next prime is 7.

53, 61, 157, 229, 307, 439, 613, 757, 769, 823, 853, 859, 883, 907, 937, 967, 1009, 1297, 1423, 1429, 1447, 1483, 1489, 1549, 1597, 1663, 1693, 1993, 2083, 2137, 2203, 2239, 2389, 2437, 2659, 2689, 2707, 2749, 2833, 2857, 2953, 3019, 3037, 3163, 3187

Offset: 1

Author

Amarnath Murthy, Sep 26 2002

Keywords

• nonn

Links

• Daria Micovic, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

Mathematica

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

Extensions

Corrected and extended by Matthew Conroy, Apr 30 2003

Name edited by Michel Marcus, May 28 2016