%I #19 Oct 30 2023 08:02:28

%S 2,3,5,7,13,19,31,53,73,89,359,139,401,181,113,211,293,661,863,773,

%T 523,1933,1831,1069,1381,887,1637,1129,1669,1951,4027,3469,4177,6397,

%U 2477,2971,5531,1327,4297,4831,5351,5591,9973,11743,13187,8467,27851,18803

%N 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.

%C a(10) > a(11).

%H Donovan Johnson, <a href="/A075580/b075580.txt">Table of n, a(n) for n = 0..257</a> (first 200 terms from T. D. Noe)

%H XIAO Gang, <a href="http://wims.unice.fr/wims/wims.cgi?session=DV2995E06F.4&amp;+lang=en&amp;+module=tool%2Falgebra%2Ffactor">Factoris, factors huge integers</a>.

%t 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 *)

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

%K nonn

%O 0,1

%A _Amarnath Murthy_, Sep 26 2002

%E Corrected and extended by _Sam Alexander_, Oct 20 2003