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%I #12 Aug 11 2019 03:40:53
%S 0,1,2,1,2,3,4,2,4,5,6,3,4,7,4,5,6,8,9,6,9,10,11,7,11,12,12,8,9,13,14,
%T 13,14,15,14,10,11,15,11,15,16,16,17,16,17,18,19,17,19,19,18,18,19,20,
%U 19,20,21,20,21,20,21,22,22,19,23,23,24,20,24,24,25,24,25,26,26,25,27
%N Number of iterations of the map n-> n - sigma(bigomega(n)) needed to reach 1.
%C The function n-A000203(A001222(n)) = 1, 1, 2, 1, 4, 3, 6, 4, 6, 7, 10, 8, 12,... (n>=1) is applied repeatedly starting at n.
%C The sequence counts the iterations needed to reach one of the 1.
%H Amiram Eldar, <a href="/A176846/b176846.txt">Table of n, a(n) for n = 1..10000</a>
%e For n = 10, a(10)= 5 because 10 - sigma(bigomega(10) = 7 (1st iter.);
%e 7 - sigma(bigomega(7)) = 6 (2nd iter.); 6 - sigma(bigomega(6)) = 3 (3rd iter.);
%e 3 - sigma(bigomega(3)) = 2 (4th iter.); 2 - sigma(bigomega(2)) = 1 (5th and last iter, reaching 1).
%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<>1) do: nn:=nn - sigma(bigomega((nn))): k:=k+1: od: tabl[n]:=k: od: print(tabl):
%t Table[Length[NestWhileList[#-DivisorSigma[1,PrimeOmega[#]]&,n,#!=1&]]-1,{n,80}] (* _Harvey P. Dale_, Aug 08 2016 *)
%Y Cf. A000203, A001222.
%K nonn,easy
%O 1,3
%A _Michel Lagneau_, Apr 27 2010
%E Unspecific reference removed by _R. J. Mathar_, Oct 20 2010
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