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

1,4

Links

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

Formula

From Amiram Eldar, Jul 18 2024:

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

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

Example

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.

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 *)

Crossrefs

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

Sequence in context: A025849 A088782 A291984 * A134024 A161069 A161108

Adjacent sequences: A066669 A066670 A066671 * A066673 A066674 A066675

Keyword

nonn

Author

Labos Elemer, Dec 18 2001

Extensions

Name corrected by Amiram Eldar, Jul 18 2024

Status

approved