A227944 Number of iterations of "take odd part of phi" (A053575) to reach 1 from n.

0, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 1, 1, 2, 3, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 1, 2, 1, 2, 1, 2, 2, 3, 3, 2, 1, 2, 2, 3, 2, 2, 3, 4, 1, 3, 2, 1, 2, 3, 3, 2, 2, 3, 3, 4, 1, 2, 2, 3, 1, 2, 2, 3, 1, 3, 2, 3, 2, 3, 3, 2, 3, 2, 2, 3, 1, 4, 2, 3, 2, 1, 3, 3, 2, 3, 2, 3, 3, 2, 4, 3, 1, 2, 3, 2, 2

Offset

1,7

Comments

a(n) >= A256757(n) - 1.

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

Formula

For n > 1, a(n) = a(A053575(n)) + 1.

Example

a(18) = 2 because it takes two steps to reach 1 from 18: phi(18) = 6, the odd part of which is 3, and phi(3) = 2, the odd part of which is 1.
a(19) = 3 because it takes three steps to reach 1 from 19: phi(19) = 18, the odd part of which is 9, and phi(9) = 6, the odd part of which is 3, and phi(3) = 2, the odd part of which is 1.

Mathematica

oddPhi[n_] := Module[{phi = EulerPhi[n]}, phi/2^IntegerExponent[phi, 2]]; Table[Length[NestWhileList[oddPhi[#] &, n, # > 1 &]] - 1, {n, 100}] (* T. D. Noe, Oct 07 2013 *)

Prog

(Haskell)
a227944 n = fst $
            until ((== 1) . snd) (\(i, x) -> (i + 1, a053575 x)) (0, n)
-- Reinhard Zumkeller, Oct 09 2013

Crossrefs

A variant of A049115: a(n) = A049115(n) unless n is a power of 2.

Cf. A003434, A227946.

Sequence in context: A295660 A193169 A193453 * A095772 A305392 A175301

Adjacent sequences: A227941 A227942 A227943 * A227945 A227946 A227947

Keyword

nonn,easy

Author

Max Alekseyev, Oct 03 2013

Status

approved