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A049093 Numbers n such that 2^n - 1 is squarefree.

%I A049093 #30 Sep 08 2022 08:44:58
%S A049093 1,2,3,4,5,7,8,9,10,11,13,14,15,16,17,19,22,23,25,26,27,28,29,31,32,
%T A049093 33,34,35,37,38,39,41,43,44,45,46,47,49,50,51,52,53,55,56,57,58,59,61,
%U A049093 62,64,65,67,68,69,70,71,73,74,75,76,77,79,81,82,83,85,86,87,88,89,91,92
%N A049093 Numbers n such that 2^n - 1 is squarefree.
%C A049093 Numbers n such that gcd(n, 2^n - 1) = 1 and n is not a multiple of A002326((q - 1)/2), where q is a Wieferich prime A001220. - _Thomas Ordowski_, Nov 21 2015
%C A049093 If n is in the sequence, then so are all divisors of n. - _Robert Israel_, Nov 23 2015
%H A049093 Max Alekseyev, <a href="/A049093/b049093.txt">Table of n, a(n) for n = 1..910</a>
%e A049093 a(7) = 8 because 2^8 - 1 = 255 = 3 * 5 * 17 is squarefree.
%p A049093 N:= 400: # to get all terms <= N
%p A049093 # This relies on the fact that the first N+1 members of A000225 have all been factored
%p A049093 # without any further Wieferich primes being found.
%p A049093 V:= Vector(N,1):
%p A049093 V[364 * [$1..N/364]]:= 0:
%p A049093 V[1755 * [$1..N/1755]]:= 0:
%p A049093 for n from 2 to N do
%p A049093 if V[n] = 0 then next fi;
%p A049093 if igcd(n, 2 &^n - 1 mod n) > 1 then
%p A049093   V[n * [$1..N/n]]:= 0
%p A049093 fi;
%p A049093 od:
%p A049093 select(t -> V[t] = 1, [$1..N]); # _Robert Israel_, Nov 23 2015
%t A049093 Select[Range@ 92, SquareFreeQ[2^# - 1] &] (* _Michael De Vlieger_, Nov 21 2015 *)
%o A049093 (PARI) isok(n) = issquarefree(2^n - 1); \\ _Michel Marcus_, Dec 19 2013
%o A049093 (Magma) [n: n in [1..100] | IsSquarefree(2^n-1)]; // _Vincenzo Librandi_, Nov 22 2015
%Y A049093 Complement of A049094.
%K A049093 nonn
%O A049093 1,2
%A A049093 _Labos Elemer_
%E A049093 Terms a(73)-a(910) in b-file from _Max Alekseyev_, Nov 15 2014, Sep 28 2015