A075585 Primes p such that the number of distinct prime divisors of all composite numbers between p and the next prime is 5.

19, 23, 37, 43, 97, 127, 223, 499, 673, 1213, 2309, 2729, 6089, 6269, 7589, 8969, 9239, 9281, 10709, 11549, 11969, 12539, 13397, 14321, 15329, 16829, 17489, 18059, 19139, 19379, 19469, 19889, 20747, 21317, 21839, 22109, 22619, 23369, 23561, 24179

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Mathematica

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A343741 A060269 A245382 * A052030 A045297 A039292

Adjacent sequences: A075582 A075583 A075584 * A075586 A075587 A075588

Keyword

nonn

Author

Amarnath Murthy, Sep 26 2002

Extensions

More terms from Sam Alexander, Oct 21 2003

Status

approved