A227946 Smallest m such that the number of iterations of "take odd part of phi" to reach 1 from m (A227944) is n.

1, 2, 7, 19, 47, 163, 487, 1307, 2879, 19683, 39367, 177147, 531441, 1594323, 4782969, 14348907, 43046721, 86093443, 258280327, 688747547, 3486784401, 10460353203

Offset: 0

Author

Max Alekseyev, Oct 03 2013

Keywords

• nonn
• more

Comments

The odd part of a number is its largest odd divisor (A000265), phi is Euler's totient function (A000010). - Alonso del Arte, Oct 13 2013

Examples

			a(1) = 2 because just one step is needed to reach 1 from 2, since phi(2) = 1. The numbers 3, 4, 5 and 6 also take one step.
a(2) = 7 because two steps are needed to reach 1 from 7: phi(7) = 6, the odd part of which is 3, and phi(3) = 2, the odd part of which is 1. The numbers from 8 to 18 take one or two steps to reach 1.
a(3) = 19 because three steps are needed 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.
		

Crossrefs

A variant of A049117. - R. J. Mathar, Oct 06 2013

Cf. A007755, A053575, A000010.

Programs

Haskell

import Data.List (elemIndex); import Data.Maybe (fromJust)
a227946 = (+ 1) . fromJust . (`elemIndex` a227944_list)
-- Reinhard Zumkeller, Nov 10 2013

Formula

a(n) = smallest m such that A227944(m)=n.

Extensions

a(15) through a(21) copied over from A049117 by Max Alekseyev, Oct 13 2013