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A238529 a(0) = a(1) = 0, and for n > 1, a(n) = number of iterations of A238525 (n modulo sopfr(n)) needed to reach either 0 or 1. Here sopfr(n) is the sum of the prime factors of n, with multiplicity, A001414.

%I A238529 #28 Oct 21 2017 21:16:03
%S A238529 0,0,1,1,1,1,1,1,2,2,2,1,2,1,2,2,1,1,2,1,2,1,3,1,2,2,2,1,2,1,1,1,2,2,
%T A238529 3,2,2,1,2,2,2,1,2,1,3,1,2,1,2,2,2,2,1,1,3,2,2,2,2,1,1,1,2,2,2,2,2,1,
%U A238529 2,2,1,1,1,1,3,3,2,2,2,1,2,3,3,1,1,2,2,2,2,1,3,2,2,3,2,2,2,1,2,3,2,1,3,1,3,1
%N A238529 a(0) = a(1) = 0, and for n > 1, a(n) = number of iterations of A238525 (n modulo sopfr(n)) needed to reach either 0 or 1. Here sopfr(n) is the sum of the prime factors of n, with multiplicity, A001414.
%C A238529 Previous name was: Recursive depth of n modulo sopfr(n), where sopfr(n) is the sum of the prime factors of n, with multiplicity.
%C A238529 Indices of records are 0, 2, 8, 22, 166, ... (A238530) - _David A. Corneth_ & _Antti Karttunen_, Oct 20 2017
%H A238529 Antti Karttunen, <a href="/A238529/b238529.txt">Table of n, a(n) for n = 0..16384</a>
%F A238529 a(0) = a(1) = 0; for n > 1, a(n) = 1 + a(A238525(n)). - _Antti Karttunen_, Oct 20 2017
%e A238529 a(2) = 1, because 2 mod sopfr(2) = 2 mod 2 = 0, and further recursion (0 mod sopfr(0)) is undefined.
%e A238529 a(8) = 2, because 8 mod sopfr(8) = 8 mod 6 = 2, and 2 mod sopfr(2) is defined as above, giving 8 a recursive depth of 2.
%t A238529 Array[-1 + Length@ NestWhileList[Mod[#, Total@ Flatten@ Map[ConstantArray[#1, #2] & @@ # &, FactorInteger@ #]] &, #, # > 1 &] &, 105, 0] (* _Michael De Vlieger_, Oct 20 2017 *)
%o A238529 (Sage)
%o A238529 def a(n):
%o A238529     d = 0
%o A238529     while n>1:
%o A238529         n = n % sum([f[0]*f[1] for f in factor(n)])
%o A238529         d = d+1
%o A238529    return d
%o A238529 # _Ralf Stephan_, Mar 09 2014
%o A238529 (PARI)
%o A238529 A001414(n) = { my(f=factor(n)); sum(k=1, matsize(f)[1], f[k, 1]*f[k, 2]); };
%o A238529 A238525(n) = (n%A001414(n));
%o A238529 A238529(n) = if(n<=1,0,1+A238529(A238525(n))); \\ _Antti Karttunen_, Oct 20 2017
%Y A238529 Cf. A001414, A238525, A238530.
%K A238529 nonn
%O A238529 0,9
%A A238529 _J. Stauduhar_, Feb 28 2014
%E A238529 More terms from _Ralf Stephan_, Mar 09 2014
%E A238529 Terms a(0) = a(1) = 0 prepended and name changed by _Antti Karttunen_, Oct 20 2017