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%I #10 Jan 21 2013 09:59:43
%S 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,
%T 10,11,11,12,12,12,12,13,13,13,14,14,14,14,14,15,15,16,15,16,16,16,17,
%U 16,17,17,18,18,19,17,19,20,20,19,21,21,20,21,20,21,21,21,22,22,21,22,22
%N The number of iterations of the map n -> n - bigomega(sigma(n)) until reaching 1.
%C 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.
%e a(n=12) = 5 because :
%e 12 - bigomega(sigma(12)) = 9 (1st step); 9 - bigomega(sigma(9)) = 8 (2nd step)
%e 8 - bigomega(sigma(8)) = 6 (3rd step); 6 - bigomega(sigma(6)) = 3 (4th step);
%e 3 - bigomega(sigma(3)) = 1 (fifth and final step).
%p with(numtheory): n0:=200:tabl:=array(1..n0):
%p 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):
%t Table[Length[NestWhileList[#-PrimeOmega[DivisorSigma[1,#]]&,n,#>1&]]- 1,{n,80}] (* _Harvey P. Dale_, Dec 16 2012 *)
%K nonn,easy
%O 1,4
%A _Michel Lagneau_, Apr 27 2010
%E Examples of the auxiliary function added - _R. J. Mathar_, Oct 12 2010
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