A242606 - OEIS

%I #15 Jan 19 2019 04:15:43

%S 1309,1442,1885,2013,2091,2665,2694,2714,3243,3422,3655,3729,3854,

%T 3855,4430,4431,4503,4921,5034,5035,5133,5282,5678,5795,5882,5883,

%U 5943,5954,6054,6061,6094,6213,6302,6303,6305,6306,6477,6851,6853,6873,6985,7202,7257,7334,7383,7682,7730,7802,7842,7922,7953,8238,8239

%N Start of a triple of consecutive squarefree numbers each of which has exactly 3 distinct prime factors.

%C Sequence A066509 is a subsequence.

%H Harvey P. Dale, <a href="/A242606/b242606.txt">Table of n, a(n) for n = 1..10000</a>

%H Daniel C. Mayer, <a href="http://www.linkedin.com/groupItem?view=&amp;gid=4510047&amp;item=5873010790079934468&amp;type=member">Define an "m-triple" to consist of three consecutive squarefree positive integers, each with exactly m prime divisors</a>, Number Theory group on LinkedIn.com

%e The two squarefree numbers following a(1)=1309=7*11*17 are 1310=2*5*131 and 1311=3*19*23, all three have 3 prime divisors.

%e The same is true for a(2)=1442, 1443 and the next squarefree number which is 1446.

%e Further examples are provided by the first "sphenic triples" (1309, 1310, 1311), (1885, 1886, 1887) and (2013, 2014, 2015).

%t Transpose[Select[Partition[Select[Range[10000],SquareFreeQ],3,1], Union[ PrimeNu[ #]] == {3}&]][[1]] (* _Harvey P. Dale_, Apr 29 2016 *)

%o (PARI) (back(n)=for(i=1,2,until(issquarefree(n--),));n);for(n=1,9999,issquarefree(n)||next;ndk==ndm&&omega(n)==ndm&&ndk==3&&print1(back(n)",");ndk=ndm;ndm=omega(n))

%Y See A242605-A242608 for triples of consecutive squarefree numbers (A005117) with m=2,...,5 prime factors; A242621 (first terms for positive m).

%K nonn

%O 1,1

%A _M. F. Hasler_, May 18 2014

%E Minor edit by _Hans Havermann_, Aug 19 2014