A176843 The number of iterations of the map n -> n - bigomega(phi(n)) until reaching 2.

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, 12, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 19, 20, 20, 21, 20, 21, 22, 22, 22, 21, 23, 23, 23, 24, 24, 24, 24, 24, 25, 25, 25, 25

Offset

2,3

Comments

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)

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

Links

Table of n, a(n) for n=2..77.

Example

a(n=8)= 4 because:
8 - bigomega(phi(8)) = 6 (1st step), 6 - bigomega(phi(6)) = 5 (2nd step),
5 - bigomega(phi(5)) = 3 (3rd step), 3 - bigomega(phi(3)) = 2 (4th and final step).

Maple

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):

Crossrefs

Sequence in context: A194253 A284849 A274618 * A238263 A071542 A264810

Adjacent sequences: A176840 A176841 A176842 * A176844 A176845 A176846

Keyword

nonn,easy

Author

Michel Lagneau, Apr 27 2010

Extensions

Undefined a(1) and unspecific reference removed - R. J. Mathar, Oct 12 2010

Status

approved