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

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, 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, 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

Offset: 1

Author

Charles R Greathouse IV, Apr 26 2016

Keywords

• nonn

Comments

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

Examples

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

Links

• Antti Karttunen (terms 1..310) & Hans Havermann, Table of n, a(n) for n = 1..1206

Crossrefs

Cf. A237043, A000225, A049094.

Programs

Maple

a:= n-> mul(i[1]^iquo(i[2], 2), i=ifactors(2^n-1)[2]):
seq(a(n), n=1..105);  # Alois P. Heinz, Apr 29 2016

Mathematica

a[n_] := Sqrt[(2^n-1)/Times @@ Power @@@ ({#[[1]], Mod[#[[2]], 2]}& /@ FactorInteger[2^n -1])];
Array[a, 105] (* Jean-François Alcover, Jan 03 2022 *)

PARI

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

Formula

a(n) = A000188(A000225(n)). - R. J. Mathar, Apr 28 2016

Extensions

More terms from Antti Karttunen, Sep 23 2018