%I #14 Dec 26 2023 11:59:36
%S 0,1,2,2,3,3,4,4,5,5,6,6,7,7,8,7,8,9,10,9,11,10,11,10,12,11,11,13,14,
%T 12,13,12,14,13,15,13,14,14,15,14,15,16,17,16,17,17,18,18,19,19,20,20,
%U 21,20,22,21,23,22,23,22,23,23,23,23,24,24,25,25,26,26
%N The number of iterations needed to reach 1 under the map n-> n-bigomega(n).
%C The map n -> A069345(n) is applied repeatedly, starting at n, until reaching a 1.
%H Enrique Pérez Herrero, <a href="/A176814/b176814.txt">Table of n, a(n) for n = 1..5000</a>
%e a(n=5) = 3 because 5 - bigomega(5) = 4 (first iteration),
%e 4 - bigomega(4) = 2 (second iteration) and
%e 2 - bigomega(2) = 1 (third iteration and reaching 1).
%p with(numtheory): n0:=200:tabl:=array(1..n0): for n from 1 to 1000 do: k:=0: nn:=n: for q from 0 to 1000 while(nn<>1) do:nn:=nn - bigomega(nn): k:=k+1: od: tabl[n]:=k: od: print(tabl):
%t t[n_] := -1 + Length[NestWhileList[#-PrimeOmega[#]&, n, #>1&]]; Table[t[n], {n,100}] (* _Enrique Pérez Herrero_, Apr 25 2012 *)
%Y Cf. A001222.
%K nonn
%O 1,3
%A _Michel Lagneau_, Apr 26 2010
%E Mention A069345 in the comment. - _R. J. Mathar_, Oct 20 2010