A242621 Start of the least triple of consecutive squarefree numbers each of which has exactly n distinct prime factors.

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

Offset: 1

Author

M. F. Hasler, May 18 2014

Keywords

• nonn

Comments

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.

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

Examples

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

Links

• Daniel C. Mayer, Define an "m-triple" to consist of three consecutive squarefree positive integers, each with exactly m prime divisors, Number Theory group on LinkedIn.com

Crossrefs

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

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

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

Extensions

Edited and a(6)-a(7) added by Hans Havermann, Aug 27 2014