A242621 - OEIS

%I #28 Apr 11 2022 22:21:26

%S 2,33,1309,27962,3323705,296602730,41704979953

%N Start of the least triple of consecutive squarefree numbers each of which has exactly n distinct prime factors.

%C As the example of a(4)=27962 shows, "consecutive squarefree numbers" means consecutive elements of A005117, not necessarily consecutive integers that (additionally) are squarefree; this would be a more restrictive condition.

%C a(8) <= 102099792179229 because A093550 - 1 is an upper bound of the present sequence.

%H Daniel C. Mayer, <a href="http://www.linkedin.com/groupItem?view=&amp;gid=4510047&amp;item=5873010790079934468&amp;type=member">Define an "m-triple" to consist of three consecutive squarefree positive integers, each with exactly m prime divisors</a>, Number Theory group on LinkedIn.com

%e The two squarefree numbers following a(4)=27962, namely, 27965 and 27966, also have 4 prime divisors just as a(4).

%Y See A242605-A242608 for triples of consecutive squarefree numbers with m=2,..,5 prime factors.

%Y See A246470 for the quadruplet and A246548 for the 5-tuple versions of this sequence.

%Y See A039833, A066509, A176167 and A192203 for triples of consecutive numbers which are squarefree and have m=2,..,5 prime factors.

%K nonn

%O 1,1

%A _M. F. Hasler_, May 18 2014

%E Edited and a(6)-a(7) added by _Hans Havermann_, Aug 27 2014