

A242606


Start of a triplet of consecutive squarefree numbers each of which has exactly 3 distinct prime factors.


3



1309, 1442, 1885, 2013, 2091, 2665, 2694, 2714, 3243, 3422, 3655, 3729, 3854, 3855, 4430, 4431, 4503, 4921, 5034, 5035, 5133, 5282, 5678, 5795, 5882, 5883, 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
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OFFSET

1,1


COMMENTS

Sequence A066509 is a subsequence.


LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..10000
Daniel C. Mayer, Define an "mtriplet" to consist of three consecutive squarefree positive integers, each with exactly m prime divisors, Number Theory group on LinkedIn.com


EXAMPLE

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.
The same is true for a(2)=1442, 1443 and the next squarefree number which is 1446.
Further examples are provided by the first "sphenic triples" (1309, 1310, 1311), (1885, 1886, 1887) and (2013, 2014, 2015).


MATHEMATICA

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


PROG

(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))


CROSSREFS

See A242605A242608 for triplets of consecutive squarefree numbers (A005117) with m=2,...,5 prime factors; A242621 (first terms for positive m).
Sequence in context: A233975 A209853 A165936 * A066509 A248202 A256668
Adjacent sequences: A242603 A242604 A242605 * A242607 A242608 A242609


KEYWORD

nonn


AUTHOR

M. F. Hasler, May 18 2014


EXTENSIONS

Minor edit by Hans Havermann, Aug 19 2014


STATUS

approved



