cp's OEIS Frontend

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.

%I A075580 #19 Oct 30 2023 08:02:28
%S A075580 2,3,5,7,13,19,31,53,73,89,359,139,401,181,113,211,293,661,863,773,
%T A075580 523,1933,1831,1069,1381,887,1637,1129,1669,1951,4027,3469,4177,6397,
%U A075580 2477,2971,5531,1327,4297,4831,5351,5591,9973,11743,13187,8467,27851,18803
%N 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.
%C A075580 a(10) > a(11).
%H A075580 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 A075580 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 A075580 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 A075580 Cf. A052297, A075581, A059960, A075583, A075584, A075585, A075586, A075587, A075588, A075589.
%K A075580 nonn
%O A075580 0,1
%A A075580 _Amarnath Murthy_, Sep 26 2002
%E A075580 Corrected and extended by _Sam Alexander_, Oct 20 2003