A069112 Squarefree part of 2^n-1 : the smallest number such that a(n)*(2^n-1) is a square.

1, 3, 7, 15, 31, 7, 127, 255, 511, 1023, 2047, 455, 8191, 16383, 32767, 65535, 131071, 29127, 524287, 41943, 42799, 4194303, 8388607, 1864135, 33554431, 67108863, 134217727, 268435455, 536870911, 119304647, 2147483647, 4294967295, 8589934591, 17179869183, 34359738367

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..1206

Formula

a(n) = A007913(A000225(n)). - Michel Marcus, Apr 10 2014

Mathematica

SquareFreePart[n_] := Times @@ Apply[Power, {First[#], Mod[Last[#], 2]}& /@ FactorInteger[n], {1}]; a[n_] := SquareFreePart[2^n-1]; Table[a[n], {n, 1, 32}] (* Jean-François Alcover, Apr 10 2014 *)

Prog

(PARI) for(n=1, 60, print1(core(2^n-1), ", "))

Crossrefs

Cf. A000225, A007913.

Sequence in context: A373089 A291754 A336685 * A064084 A090633 A320024

Adjacent sequences: A069109 A069110 A069111 * A069113 A069114 A069115

Keyword

nonn

Author

Benoit Cloitre, Apr 06 2002

Extensions

More terms from Amiram Eldar, Sep 05 2020

Status

approved