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

%I A260042 #36 Sep 08 2022 08:46:13
%S A260042 9,10,18,20,21,27,30,36,40,42,45,50,54,55,60,63,68,70,72,78,80,81,84,
%T A260042 90,99,100,105,108,110,117,120,126,130,135,136,140,144,147,150,153,
%U A260042 155,156,160,162,165,168,170,171,180,182,189,190,198,200,204,207,210
%N A260042 Numbers k such that (4^k-1)/3 is not squarefree.
%C A260042 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
%C A260042 Complement of A259178. - _Omar E. Pol_, Aug 03 2015
%D A260042 James R. Buddenhagen, Posting to Math Fun Mailing List, Jul 22 2015.
%H A260042 Amiram Eldar, <a href="/A260042/b260042.txt">Table of n, a(n) for n = 1..169</a>
%e A260042 (4^9-1)/3 = 3^2*7*19*73 is not squarefree, so 9 is in the sequence. - _R. J. Mathar_, Aug 02 2015
%t A260042 Select[Range[120],!SquareFreeQ[(4^#-1)/3]&] (* _Ivan N. Ianakiev_, Jul 23 2015 *)
%o A260042 (Magma) [n: n in [1..120]| not IsSquarefree((4^n-1) div 3)]; // _Vincenzo Librandi_, Jul 27 2015
%o A260042 (PARI) isok(k) = !issquarefree((4^k-1)/3); \\ _Michel Marcus_, Feb 25 2021
%Y A260042 Cf. A002450, A005117, A013929, A259178.
%K A260042 nonn
%O A260042 1,1
%A A260042 _N. J. A. Sloane_, Jul 22 2015
%E A260042 a(24)-a(31) from _Ivan N. Ianakiev_, Jul 23 2015
%E A260042 a(32)-a(45) from _Chai Wah Wu_, Jul 26 2015
%E A260042 a(46)-a(57) from _Lars Blomberg_, Aug 06 2017