A064085 Quotient of A000225 and A064084.

1, 1, 1, 1, 1, 3, 1, 1, 1, 11, 1, 39, 1, 43, 151, 1, 1, 171, 1, 2255, 2359, 683, 1, 9399, 1, 2731, 1, 140911, 1, 1649373, 1, 1, 599479, 43691, 8727391, 8965359, 1, 174763, 9588151, 139090655, 1, 1649061309, 1, 572942063, 2221095391, 2796203, 1

Offset: 1

Author

Jens Voß, Sep 04 2001

Keywords

• easy
• nonn

Comments

a(n) is equal to 1 if and only if n is a prime power; the sequence of nontrivial values of a is A064086.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000225, A064084, A064086.

Programs

Maple

a:= n-> (2^n-1)/mul(2^(i[1]^i[2])-1, i=ifactors(n)[2]):
seq(a(n), n=1..50);  # Alois P. Heinz, Jun 09 2014

Mathematica

a[n_] := (2^n-1)/Times @@ (2^(Power @@@ FactorInteger[n])-1);
Table[a[n], {n, 1, 50}] (* Jean-François Alcover, Jan 13 2025 *)

Formula

a(n) = A000225(n) / A064084(n).

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 29 2003