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A260042
Numbers k such that (4^k-1)/3 is not squarefree.
2
9, 10, 18, 20, 21, 27, 30, 36, 40, 42, 45, 50, 54, 55, 60, 63, 68, 70, 72, 78, 80, 81, 84, 90, 99, 100, 105, 108, 110, 117, 120, 126, 130, 135, 136, 140, 144, 147, 150, 153, 155, 156, 160, 162, 165, 168, 170, 171, 180, 182, 189, 190, 198, 200, 204, 207, 210
OFFSET
1,1
COMMENTS
Contains all positive multiples of 9 (A008591), because 4^n-1 == 0 (mod 27) for these and (4^n-1)/3 is a multiple of 3^2 then. Contains also all positive multiples of 10 (A008592), because 4^n-1 == 0 (mod 125) for these and (4^n-1)/3 is a multiple of 5^2 then. Contains all positive multiples of 21 (A008603), because 4^n-1 == 0 (mod 147) for these and (4^n-1)/3 is a multiple of 7^2 then. - R. J. Mathar, Aug 02 2015
Complement of A259178. - Omar E. Pol, Aug 03 2015
REFERENCES
James R. Buddenhagen, Posting to Math Fun Mailing List, Jul 22 2015.
LINKS
EXAMPLE
(4^9-1)/3 = 3^2*7*19*73 is not squarefree, so 9 is in the sequence. - R. J. Mathar, Aug 02 2015
MATHEMATICA
Select[Range[120], !SquareFreeQ[(4^#-1)/3]&] (* Ivan N. Ianakiev, Jul 23 2015 *)
PROG
(Magma) [n: n in [1..120]| not IsSquarefree((4^n-1) div 3)]; // Vincenzo Librandi, Jul 27 2015
(PARI) isok(k) = !issquarefree((4^k-1)/3); \\ Michel Marcus, Feb 25 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jul 22 2015
EXTENSIONS
a(24)-a(31) from Ivan N. Ianakiev, Jul 23 2015
a(32)-a(45) from Chai Wah Wu, Jul 26 2015
a(46)-a(57) from Lars Blomberg, Aug 06 2017
STATUS
approved