login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A188047 Numbers k such that k^k-1 and k^k+1 are squarefree. 1
2, 4, 6, 12, 16, 20, 22, 34, 36, 42, 52, 56, 58, 60, 66, 72, 78, 84, 86, 88, 90, 92, 94, 96, 102, 104, 106, 108, 110, 112, 114, 128, 138, 140, 142, 144, 156, 158 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
From Kevin P. Thompson, May 03 2022: (Start)
a(39) >= 160 (160^160-1 is squarefree; 160^160+1 has no known square factors but is not completely factored).
162, 186, 198, and 256 are also terms in this sequence. (End)
LINKS
EXAMPLE
6 is a term since 6^6-1 = 46655 = 5*7*31*43 and 6^6+1 = 46657 = 13*37*97 are both squarefree.
MATHEMATICA
Select[Range@42, SquareFreeQ[#^#-1]&&SquareFreeQ[#^#+1]&]
PROG
(PARI) isok(k) = issquarefree(k^k-1) && issquarefree(k^k+1); \\ Michel Marcus, Feb 22 2021
CROSSREFS
Intersection of A184966 and A184967.
Cf. A005117.
Sequence in context: A309096 A019280 A090748 * A032465 A089395 A089699
KEYWORD
nonn,hard,more
AUTHOR
EXTENSIONS
a(11)-a(25) from D. S. McNeil, Mar 22 2011
a(26)-a(31) from Amiram Eldar, Feb 22 2021
a(32)-a(38) (from FactorDB) added by Kevin P. Thompson, May 03 2022
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 3 15:08 EST 2024. Contains 370512 sequences. (Running on oeis4.)