A176843 - OEIS

%I #4 Mar 30 2012 18:35:53

%S 0,1,2,2,3,3,4,4,5,5,6,6,7,7,7,7,8,8,8,9,9,10,10,10,11,11,11,12,12,12,

%T 12,13,13,13,14,14,14,14,15,15,15,16,16,16,17,17,17,18,18,18,18,19,19,

%U 19,19,20,20,21,20,21,22,22,22,21,23,23,23,24,24,24,24,24,25,25,25,25

%N The number of iterations of the map n -> n - bigomega(phi(n)) until reaching 2.

%C The function n-bigomega(phi(n)) = n-A001222(A000010(n)) = 0, 1, 2, 2, 3, 3, 5, 5, 6, 7, 8, 9, 10, 10,... (n>=0)

%C is iterated until one of the 2's is reached.

%e a(n=8)= 4 because:

%e 8 - bigomega(phi(8)) = 6 (1st step), 6 - bigomega(phi(6)) = 5 (2nd step),

%e 5 - bigomega(phi(5)) = 3 (3rd step), 3 - bigomega(phi(3)) = 2 (4th and final step).

%p with(numtheory): n0:=200:tabl:=array(1..n0): for n from 1 to n0 do:k:=0:nn:=n:for q from 0 to 1000 while(nn<>2 and n<>1) do:nn:=nn - bigomega(phi((nn))):k:=k+1:od:tabl[n]:=k:od:print(tabl):

%K nonn,easy

%O 2,3

%A _Michel Lagneau_, Apr 27 2010

%E Undefined a(1) and unspecific reference removed - _R. J. Mathar_, Oct 12 2010