A075580 Smallest prime p(k) such that the number of distinct prime divisors of all composite numbers between p(k) and p(k+1) is n.

2, 3, 5, 7, 13, 19, 31, 53, 73, 89, 359, 139, 401, 181, 113, 211, 293, 661, 863, 773, 523, 1933, 1831, 1069, 1381, 887, 1637, 1129, 1669, 1951, 4027, 3469, 4177, 6397, 2477, 2971, 5531, 1327, 4297, 4831, 5351, 5591, 9973, 11743, 13187, 8467, 27851, 18803

Offset: 0

Author

Amarnath Murthy, Sep 26 2002

Keywords

• nonn

Comments

a(10) > a(11).

Links

• Donovan Johnson, Table of n, a(n) for n = 0..257 (first 200 terms from T. D. Noe)
• XIAO Gang, Factoris, factors huge integers.

Crossrefs

Cf. A052297, A075581, A059960, A075583, A075584, A075585, A075586, A075587, A075588, A075589.

Programs

Mathematica

Table[i=1; While[Length[Union[Flatten[Table[First/@FactorInteger[j],{j,(x=Prime[i])+1,NextPrime[x]-1}]]]]!=n,i++]; x,{n,0,47}] (* Jayanta Basu, May 25 2013 *)

Extensions

Corrected and extended by Sam Alexander, Oct 20 2003