A176844 The number of iterations of the map n -> n - bigomega(sigma(n)) until reaching 1.

0, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 7, 7, 7, 7, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 11, 10, 11, 11, 12, 12, 12, 12, 13, 13, 13, 14, 14, 14, 14, 14, 15, 15, 16, 15, 16, 16, 16, 17, 16, 17, 17, 18, 18, 19, 17, 19, 20, 20, 19, 21, 21, 20, 21, 20, 21, 21, 21, 22, 22, 21, 22, 22

Offset

1,4

Comments

The function n-bigomega(sigma(n)) = n - A001222(A000203(n)) = 1, 1, 1, 3, 3, 3, 4, 6, 8, 7, 8, 9, 11, 10, 11, 15, 14, 16, 16... (n>=1) is iterated until reaching one of the 1's.

Links

Table of n, a(n) for n=1..79.

Example

a(n=12) = 5 because :
12 - bigomega(sigma(12)) = 9 (1st step); 9 - bigomega(sigma(9)) = 8 (2nd step)
8 - bigomega(sigma(8)) = 6 (3rd step); 6 - bigomega(sigma(6)) = 3 (4th step);
3 - bigomega(sigma(3)) = 1 (fifth 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<>1) do: nn:=nn - bigomega(sigma((nn))): k:=k+1: od: tabl[n]:=k: od: print(tabl):

Mathematica

Table[Length[NestWhileList[#-PrimeOmega[DivisorSigma[1, #]]&, n, #>1&]]- 1, {n, 80}] (* Harvey P. Dale, Dec 16 2012 *)

Crossrefs

Sequence in context: A039730 A257807 A152595 * A085182 A211339 A087739

Adjacent sequences: A176841 A176842 A176843 * A176845 A176846 A176847

Keyword

nonn,easy

Author

Michel Lagneau, Apr 27 2010

Extensions

Examples of the auxiliary function added - R. J. Mathar, Oct 12 2010

Status

approved