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A272334 Square root of the largest square dividing 2^n - 1.

%I A272334 #28 Jan 03 2022 11:12:59
%S A272334 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 A272334 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 A272334 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 A272334 Square root of the largest square dividing 2^n - 1.
%C A272334 a(n) > 1 if and only if n is in A049094.
%H A272334 Antti Karttunen (terms 1..310) & Hans Havermann, <a href="/A272334/b272334.txt">Table of n, a(n) for n = 1..1206</a>
%F A272334 a(n) = A000188(A000225(n)). - _R. J. Mathar_, Apr 28 2016
%e A272334 2^42 - 1 = 3^2 * 7^2 * 43 * 127 * 337 * 5419, so a(42) = 3*7 = 21.
%p A272334 a:= n-> mul(i[1]^iquo(i[2], 2), i=ifactors(2^n-1)[2]):
%p A272334 seq(a(n), n=1..105);  # _Alois P. Heinz_, Apr 29 2016
%t A272334 a[n_] := Sqrt[(2^n-1)/Times @@ Power @@@ ({#[[1]], Mod[#[[2]], 2]}& /@ FactorInteger[2^n -1])];
%t A272334 Array[a, 105] (* _Jean-François Alcover_, Jan 03 2022 *)
%o A272334 (PARI) a(n)=core(2^n-1,1)[2]
%Y A272334 Cf. A237043, A000225, A049094.
%K A272334 nonn
%O A272334 1,6
%A A272334 _Charles R Greathouse IV_, Apr 26 2016
%E A272334 More terms from _Antti Karttunen_, Sep 23 2018