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A073855 Number of steps to reach 0 starting with n and applying the process x ->bigomega(x), where bigomega = A001222.

%I A073855 #25 Jul 31 2017 14:12:43
%S A073855 0,1,2,2,3,2,3,2,3,3,3,2,3,2,3,3,4,2,3,2,3,3,3,2,4,3,3,3,3,2,3,2,3,3,
%T A073855 3,3,4,2,3,3,4,2,3,2,3,3,3,2,3,3,3,3,3,2,4,3,4,3,3,2,4,2,3,3,4,3,3,2,
%U A073855 3,3,3,2,3,2,3,3,3,3,3,2,3,4,3,2,4,3,3,3,4,2,4,3,3,3,3,3,4,2,3,3,4,2,3,2,4,3
%N A073855 Number of steps to reach 0 starting with n and applying the process x ->bigomega(x), where bigomega = A001222.
%H A073855 Antti Karttunen, <a href="/A073855/b073855.txt">Table of n, a(n) for n = 0..10000</a>
%H A073855 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>
%F A073855 a(n) = 1+A036430(n).
%F A073855 For n >= 1, a(n) = 1 + a(bigomega(n)). - _Vladeta Jovovic_, Jul 10 2004
%F A073855 With a(0) = 0 as the termination condition of the recurrence. - _Antti Karttunen_, Jul 28 2017
%e A073855 bigomega(36) = 4, bigomega(4) = 2, bigomega(2) = 1, bigomega(1) = 0, hence a(36) = 4.
%p A073855 A073855 := proc(n)
%p A073855     option remember;
%p A073855     if n <=0 then
%p A073855         0;
%p A073855     else
%p A073855         1+procname(numtheory[bigomega](n)) ;
%p A073855     end if;
%p A073855 end proc:
%p A073855 seq(A073855(n),n=0..20) ; # _R. J. Mathar_, Jul 31 2017
%t A073855 Table[-1 + Length@ NestWhileList[PrimeOmega, n, # > 0 &], {n, 0, 105}] (* _Michael De Vlieger_, Jul 29 2017 *)
%o A073855 (PARI) a(n)=if(n<=0,0,s=n; c=1; while(bigomega(s)>0,s=bigomega(s); c++); c)
%o A073855 (PARI) A073855(n) = if(!n,n,1+A073855(bigomega(n))); \\ _Antti Karttunen_, Jul 28 2017
%o A073855 (PARI) first(n) = my(v = vector(n-1)); v[1] = 1; for(i=2, #v, v[i] = 1 + v[bigomega(i)]); concat([0], v) \\ _David A. Corneth_, Jul 28 2017
%Y A073855 Cf. A001222, A036430.
%K A073855 easy,nonn
%O A073855 0,3
%A A073855 _Benoit Cloitre_, Sep 02 2002
%E A073855 More terms from _Vladeta Jovovic_, Jul 10 2004
%E A073855 Term a(0)=0 prepended by _Antti Karttunen_, Jul 28 2017