A242608 Start of a triple of consecutive squarefree numbers each of which has exactly 5 distinct prime factors.

3323705, 3875934, 4393190, 4463822, 4929470, 5401626, 5654802, 6452535, 6465414, 6800934, 7427042, 7755890, 8233743, 8343906, 8406174, 8457942, 8593802, 8716323, 9186474, 9688382, 9812582, 9965415, 10364934, 10504074, 10870563, 10977834, 11460666, 11685894, 11993462, 12474602, 13151761

Offset: 1

Author

M. F. Hasler, May 18 2014

Keywords

• nonn

Comments

See sequences A242605-A242607 (analog for m=2,3,4) for further information and examples; A242621 (first terms for positive m).

The definition of A192203 is more restrictive and therefore A192203 is a subsequence of this one, and A192203(1) >> A242608(1), roughly by a factor 5.

Examples

			a(1) = 3323705 = 5*7*11*89*97, a(1)+1 = 2*3*41*59*229 and a(1)+5 = 2*5*13*37*691 yield the first triple of consecutive squarefree numbers such that each of them is the product of five distinct primes.
		

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

Programs

PARI

(back(n)=for(i=1,2,until(issquarefree(n--),));n);for(n=10^6,2e7,issquarefree(n)||next;ndk==ndm&&ndk==5&&omega(n)==ndm&&print1(back(n)",");ndk=ndm;ndm=omega(n))

Extensions

Minor edit by Hans Havermann, Aug 19 2014