A260042 Numbers k such that (4^k-1)/3 is not squarefree.

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

Amiram Eldar, Table of n, a(n) for n = 1..169

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

Cf. A002450, A005117, A013929, A259178.

Sequence in context: A268135 A058369 A110939 * A141640 A231504 A298979

Adjacent sequences: A260039 A260040 A260041 * A260043 A260044 A260045

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