A075585 - OEIS

%I #16 Sep 08 2022 08:45:07

%S 19,23,37,43,97,127,223,499,673,1213,2309,2729,6089,6269,7589,8969,

%T 9239,9281,10709,11549,11969,12539,13397,14321,15329,16829,17489,

%U 18059,19139,19379,19469,19889,20747,21317,21839,22109,22619,23369,23561,24179

%N Primes p such that the number of distinct prime divisors of all composite numbers between p and the next prime is 5.

%H Amiram Eldar, <a href="/A075585/b075585.txt">Table of n, a(n) for n = 1..10000</a>

%t dpd5Q[p_]:=Length[Union[Flatten[FactorInteger[#][[All,1]]&/@Range[ p+1,NextPrime[ p]-1]]]]==5; Select[Prime[Range[3000]],dpd5Q] (* _Harvey P. Dale_, Aug 11 2021 *)

%o (Magma) a:=[]; for k in PrimesInInterval(2,25000) do b:={}; for s in [k..NextPrime(k)-1] do if not IsPrime(s) then b:=b join Set(PrimeDivisors(s)); end if; end for; if #Set(b) eq 5 then  Append(~a,k); end if; end for; a; // _Marius A. Burtea_, Sep 26 2019

%Y Cf. A052297, A075581, A075580, A059960, A075583, A075584, A075586, A075587, A075588, A075589.

%K nonn

%O 1,1

%A _Amarnath Murthy_, Sep 26 2002

%E More terms from _Sam Alexander_, Oct 21 2003