A176842 The number of iterations of the map x -> x - phi(bigomega(x)) needed to reach 1 starting at x=n.

0, 1, 2, 3, 4, 5, 6, 6, 7, 8, 9, 9, 10, 11, 12, 12, 13, 13, 14, 14, 15, 16, 17, 17, 18, 19, 19, 20, 21, 21, 22, 21, 22, 23, 24, 24, 25, 26, 27, 27, 28, 28, 29, 29, 30, 31, 32, 30, 31, 31, 32, 32, 33, 33, 34, 34, 35, 36, 37, 37, 38, 39, 39, 40, 41, 41, 42, 42, 43, 43, 44, 43, 44

Offset

1,3

Comments

bigomega is A001222, and phi is the Euler totient function A000010.

Links

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

Example

Starting with n = 6, a(6)=5 iterations are needed because :
f(6) = 6 - phi(bigomega(6)) = 6 - phi(2) = 6 - 1 = 5;
f(5) = 5 - phi(bigomega(5)) = 5 - phi(1) = 5 - 1 = 4;
f(4) = 4 - phi(bigomega(4)) = 4 - phi(2) = 4 - 1 = 3;
f(3) = 3 - phi(bigomega(3)) = 3 - phi(1) = 3 - 1 = 2 ;
f(2) = 2 - phi(bigomega(2)) = 2 - phi(1) = 2 - 1 = 1, and a(6) = 5.

Maple

A176842 := proc(n)
    local it, nmap ;
    it := 0 ;
    nmap := n ;
    while nmap <> 1 do
        nmap := nmap-numtheory[phi](numtheory[bigomega](nmap)) ;
        it := it+1 ;
    end do:
    it ;
end proc: # R. J. Mathar, Jun 01 2011

Mathematica

f[n_] := n - EulerPhi[PrimeOmega[n]]; a[n_] := Length[FixedPointList[f, n]] - 2; Array[a, 50] (* Amiram Eldar, Jul 13 2019 *)

Crossrefs

Sequence in context: A071520 A195918 A371156 * A278055 A291764 A319681

Adjacent sequences: A176839 A176840 A176841 * A176843 A176844 A176845

Keyword

nonn,easy

Author

Michel Lagneau, Apr 27 2010

Status

approved