A242606 Start of a triple of consecutive squarefree numbers each of which has exactly 3 distinct prime factors.

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

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 "m-triple" 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 A242605-A242608 for triples 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