A069111 Squarefree part of 2^n+1 : the smallest number such that a(n)*(2^n+1) is a square.

2, 3, 5, 1, 17, 33, 65, 129, 257, 57, 41, 2049, 4097, 8193, 16385, 3641, 65537, 131073, 262145, 524289, 1048577, 233017, 4194305, 8388609, 16777217, 33554433, 67108865, 1657009, 268435457, 536870913, 42949673, 2147483649, 4294967297, 954437177, 17179869185

Offset

0,1

Links

Amiram Eldar, Table of n, a(n) for n = 0..1062

Formula

a(n) = A007913(A000051(n)). - Amiram Eldar, Sep 05 2020

Maple

A069111 := proc(n)
    A007913(2^n+1) ;
end proc:
seq(A069111(n), n=0..30) ; # R. J. Mathar, Apr 24 2017

Mathematica

core[n_] := Module[{p, e}, Product[{p, e} = pe; p^Mod[e, 2], {pe, FactorInteger[n]}]];
a[n_] := core[2^n + 1];
a /@ Range[0, 34] (* Jean-François Alcover, May 21 2020 *)

Prog

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

Crossrefs

Cf. A000051, A007913.

Sequence in context: A262341 A178763 A111141 * A171035 A094122 A280185

Adjacent sequences: A069108 A069109 A069110 * A069112 A069113 A069114

Keyword

nonn

Author

Benoit Cloitre, Apr 06 2002

Extensions

a(0)=2 prepended by Alois P. Heinz, Apr 01 2016

Status

approved