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Square root of the largest square dividing 2^n - 1.
1

%I #28 Jan 03 2022 11:12:59

%S 1,1,1,1,1,3,1,1,1,1,1,3,1,1,1,1,1,3,1,5,7,1,1,3,1,1,1,1,1,3,1,1,1,1,

%T 1,3,1,1,1,5,1,21,1,1,1,1,1,3,1,1,1,1,1,9,1,1,1,1,1,15,1,1,7,1,1,3,1,

%U 1,1,1,1,3,1,1,1,1,1,3,1,5,1,1,1,21,1,1,1,1,1,3,1,1,1,1,1,3,1,1,1,5,1,3,1,1,7

%N Square root of the largest square dividing 2^n - 1.

%C a(n) > 1 if and only if n is in A049094.

%H Antti Karttunen (terms 1..310) & Hans Havermann, <a href="/A272334/b272334.txt">Table of n, a(n) for n = 1..1206</a>

%F a(n) = A000188(A000225(n)). - _R. J. Mathar_, Apr 28 2016

%e 2^42 - 1 = 3^2 * 7^2 * 43 * 127 * 337 * 5419, so a(42) = 3*7 = 21.

%p a:= n-> mul(i[1]^iquo(i[2], 2), i=ifactors(2^n-1)[2]):

%p seq(a(n), n=1..105); # _Alois P. Heinz_, Apr 29 2016

%t a[n_] := Sqrt[(2^n-1)/Times @@ Power @@@ ({#[[1]], Mod[#[[2]], 2]}& /@ FactorInteger[2^n -1])];

%t Array[a, 105] (* _Jean-François Alcover_, Jan 03 2022 *)

%o (PARI) a(n)=core(2^n-1,1)[2]

%Y Cf. A237043, A000225, A049094.

%K nonn

%O 1,6

%A _Charles R Greathouse IV_, Apr 26 2016

%E More terms from _Antti Karttunen_, Sep 23 2018