

A242608


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


7



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
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OFFSET

1,1


COMMENTS

See sequences A242605A242607 (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 "mtriple" 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



