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

1,1

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.

Links

Table of n, a(n) for n=1..31.

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

Example

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.

Prog

(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))

Crossrefs

Sequence in context: A186594 A244574 A250675 * A206511 A238153 A083635

Adjacent sequences: A242605 A242606 A242607 * A242609 A242610 A242611

Keyword

nonn

Author

M. F. Hasler, May 18 2014

Extensions

Minor edit by Hans Havermann, Aug 19 2014

Status

approved