A242607 Start of a triple of consecutive squarefree numbers each of which has exactly 4 distinct prime factors.

27962, 37145, 39234, 42182, 50138, 51986, 58562, 62643, 64074, 83082, 84774, 89089, 95642, 120783, 123486, 133903, 134826, 146165, 149606, 153543, 159182, 166495, 170751, 176754, 177122, 178086, 178087, 179330, 180782, 203433, 207974, 211562, 212583, 214489, 219063, 219894, 219963, 225069, 228135

Offset: 1

Author

M. F. Hasler, May 18 2014

Keywords

• nonn

Examples

			The two squarefree numbers following a(1)=27962, 27965 and 27966, also have 4 prime divisors just as a(1).
		

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 squarefree triples with m = 2..5 prime factors; A242621 (first terms for positive m).

Programs

Mathematica

Transpose[Select[Partition[Select[Range[230000],SquareFreeQ],3,1], PrimeNu[ #] =={4,4,4}&]][[1]] (* Harvey P. Dale, Jul 06 2014 *)

PARI

(back(n)=for(i=1,2,until(issquarefree(n--),));n);for(n=1,9999,issquarefree(n)||next;ndk==ndm&&omega(n)==ndm&&ndk==4&&print1(back(n)",");ndk=ndm;ndm=omega(n))

Extensions

Minor edit by Hans Havermann, Aug 19 2014