A066672 Exponent of the largest power of 2 that divides phi(A066669(n)).

1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 2, 2, 2, 3, 2, 3, 3, 2, 2, 3, 1, 1, 2, 3, 2, 3, 3, 2, 1, 4, 2, 2, 3, 3, 3, 3, 3, 1, 3, 3, 3, 3, 3, 2, 1, 5, 3, 4, 4, 2, 1, 3, 4, 4, 3, 3, 1, 5, 4, 4, 3, 3, 2, 4, 2, 4, 4, 2, 3, 5, 4, 3, 4, 4, 1, 1, 4, 2, 3, 4, 2, 3, 1, 4, 3, 5, 2, 6, 5, 5, 4, 5, 5, 4, 3, 1, 4, 6, 5, 4, 1, 3, 4, 3

Offset: 1

Author

Labos Elemer, Dec 18 2001

Keywords

• nonn

Examples

			A066669(263) = 769 and phi(769) = 768 = 3*256, so a(263) = log_2(256) = log_2(phi(769)/3) = log_2(phi(A066669(263))/A066670(263)) = 8.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A007814, A053574, A066669, A066670, A066671.

Programs

Mathematica

f[n_] := Module[{phi = EulerPhi[n], e}, e = IntegerExponent[phi, 2]; If[PrimeQ[phi/2^e], e, Nothing]]; Array[f, 300] (* Amiram Eldar, Jul 18 2024 *)

Formula

From Amiram Eldar, Jul 18 2024: (Start)

a(n) = A053574(A066669(n)).

a(n) = log_2(A066671(n)) = A007814(A000010(A066669(n))). (End)

Extensions

Name corrected by Amiram Eldar, Jul 18 2024