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A340967 a(n) is the number of iterations of the map x -> n mod sopfr(x) starting with n to reach 0 or 1, where sopfr = A001414.

%I A340967 #16 Feb 01 2021 13:28:13
%S A340967 0,1,1,1,1,1,1,2,2,2,1,3,1,4,2,1,1,2,1,2,1,4,1,3,2,4,1,3,1,1,1,2,3,3,
%T A340967 3,2,1,4,4,3,1,3,1,4,1,3,1,2,2,2,4,1,1,5,3,2,4,4,1,1,1,4,4,2,4,2,1,4,
%U A340967 2,1,1,1,1,3,3,3,3,3,1,2,3,3,1,1,3,4,5,2,1,3,3,3,3,5,4,2,1,2,2
%N A340967 a(n) is the number of iterations of the map x -> n mod sopfr(x) starting with n to reach 0 or 1, where sopfr = A001414.
%C A340967 If n is prime, or n is in A164643, then a(n) = 1.
%H A340967 Robert Israel, <a href="/A340967/b340967.txt">Table of n, a(n) for n = 1..10000</a>
%e A340967 a(12) = 3 because 12 mod (2+2+3) = 5, 12 mod 5 = 2 and 12 mod 2 = 0 (3 iterations).
%e A340967 a(54) = 5 because 54 mod (2+3+3+3) = 10, 54 mod (2+5) = 6, 54 mod 5 = 4, 54 mod (2+2) = 2, and 54 mod 2 = 0 (5 iterations).
%p A340967 sopfr:= proc(n) local t;
%p A340967   add(t[1]*t[2], t = ifactors(n)[2])
%p A340967 end proc:
%p A340967 f:= proc(n) local x,k;
%p A340967   x:= n;
%p A340967   for k from 1 do x:= n mod sopfr(x); if x <= 1 then return k fi od;
%p A340967 end proc:
%p A340967 f(1):= 0:
%p A340967 map(f, [$1..200]);
%o A340967 (Python)
%o A340967 from sympy import factorint
%o A340967 def A340967(n):
%o A340967     c, x = 0, n
%o A340967     while x > 1:
%o A340967         c += 1
%o A340967         x = n % sum(p*e for p, e in factorint(x).items())
%o A340967     return c # _Chai Wah Wu_, Feb 01 2021
%Y A340967 Cf. A001414, A164643, A340969.
%K A340967 nonn
%O A340967 1,8
%A A340967 _J. M. Bergot_ and _Robert Israel_, Jan 31 2021