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A286104 If A286103(A285734(n)) < A286103(A285735(n)), a(n) = A285734(n), otherwise a(n) = A285735(n), a(1) = 0.

%I A286104 #23 May 07 2021 12:34:32
%S A286104 0,1,1,2,3,3,2,3,3,5,6,6,7,7,5,6,7,7,6,10,11,11,13,13,14,13,14,14,15,
%T A286104 15,17,17,19,17,14,19,15,19,17,19,19,21,22,22,23,23,26,26,26,29,29,26,
%U A286104 30,31,29,30,31,29,30,30,31,31,33,33,34,33,34,34,35,35,37,37,38,37,38,38,39,39,41,41,39,41,41,42,43,43,41,46,46,47,38,46,47,47,53,53
%N A286104 If A286103(A285734(n)) < A286103(A285735(n)), a(n) = A285734(n), otherwise a(n) = A285735(n), a(1) = 0.
%C A286104 After the initial zero, all terms are squarefree numbers (A005117).
%H A286104 Antti Karttunen, <a href="/A286104/b286104.txt">Table of n, a(n) for n = 1..10000</a>
%F A286104 a(1) = 0, and for n > 1, if A286103(A285734(n)) < A286103(A285735(n)), a(n) = A285734(n), otherwise a(n) = A285735(n).
%o A286104 (Scheme) (define (A286104 n) (cond ((= 1 n) 0) ((< (A286103 (A285734 n)) (A286103 (A285735 n))) (A285734 n)) (else (A285735 n))))
%o A286104 (Python)
%o A286104 from sympy.ntheory.factor_ import core
%o A286104 def issquarefree(n): return core(n) == n
%o A286104 def a285734(n):
%o A286104     if n==1: return 0
%o A286104     j=n//2
%o A286104     while True:
%o A286104         if issquarefree(j) and issquarefree(n - j): return j
%o A286104         else: j-=1
%o A286104 def a285735(n): return n - a285734(n)
%o A286104 def a286103(n): return 0 if n==1 else 1 + min(a286103(a285734(n)), a286103(a285735(n)))
%o A286104 def a286104(n): return 0 if n==1 else  a285734(n) if a286103(a285734(n)) < a286103(a285735(n)) else a285735(n)
%o A286104 print([a286104(n) for n in range(1, 121)]) # _Indranil Ghosh_, May 02 2017
%Y A286104 Cf. A005117, A285734, A285735, A286103, A286107.
%K A286104 nonn
%O A286104 1,4
%A A286104 _Antti Karttunen_, May 02 2017