A161818 If b(n) = the largest proper divisor of n, then a(n) = (2^n - 1)/(2^b(n) - 1).

3, 7, 5, 31, 9, 127, 17, 73, 33, 2047, 65, 8191, 129, 1057, 257, 131071, 513, 524287, 1025, 16513, 2049, 8388607, 4097, 1082401, 8193, 262657, 16385, 536870911, 32769, 2147483647, 65537, 4196353, 131073, 270549121, 262145, 137438953471, 524289

Offset

2,1

Links

Alois P. Heinz, Table of n, a(n) for n = 2..1000

Example

a(6) = (2^6 - 1)/(2^3 - 1) = 63/7 = 9. - Emeric Deutsch, Jun 26 2009

Maple

with(numtheory): a := proc (n) options operator, arrow: (2^n-1)/(2^divisors(n)[tau(n)-1]-1) end proc: seq(a(n), n = 2 .. 40); # Emeric Deutsch, Jun 26 2009

Mathematica

b[n_] := Divisors[n][[-2]];
a[n_] := (2^n - 1)/(2^b[n] - 1);
a /@ Range[2, 40] (* Jean-François Alcover, Nov 20 2020 *)

Prog

(PARI) a(n) = my(d=divisors(n)); (2^n-1)/(2^d[#d-1]-1); \\ Michel Marcus, Nov 20 2020

Crossrefs

Cf. A032742.

Sequence in context: A048857 A005420 A212953 * A161509 A108974 A106853

Adjacent sequences: A161815 A161816 A161817 * A161819 A161820 A161821

Keyword

nonn

Author

Leroy Quet, Jun 20 2009

Extensions

Extended by Emeric Deutsch, Jun 26 2009

Status

approved