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A176844
The number of iterations of the map n -> n - bigomega(sigma(n)) until reaching 1.
0
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.
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
KEYWORD
nonn,easy
AUTHOR
Michel Lagneau, Apr 27 2010
EXTENSIONS
Examples of the auxiliary function added - R. J. Mathar, Oct 12 2010
STATUS
approved