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A286107 a(1) = 0, for n > 1, if A286106(n) > 0, then a(n) = A285735(n), otherwise a(n) = A285734(n).

%I A286107 #17 Apr 30 2021 06:05:26
%S A286107 0,1,2,2,3,3,5,5,6,5,5,6,7,7,10,10,7,7,13,10,10,11,13,13,14,13,13,14,
%T A286107 14,15,14,15,19,17,14,19,15,19,17,19,19,21,21,22,23,23,26,26,23,29,29,
%U A286107 26,23,23,26,26,26,29,29,30,30,31,33,33,31,33,33,34,34,35,34,35,38,37,38,38,38,39,38,41,39,41,41,42,42,43,41,46,46,47,38,46,46,47
%N A286107 a(1) = 0, for n > 1, if A286106(n) > 0, then a(n) = A285735(n), otherwise a(n) = A285734(n).
%C A286107 After the initial zero, all terms are squarefree numbers (A005117).
%H A286107 Antti Karttunen, <a href="/A286107/b286107.txt">Table of n, a(n) for n = 1..10000</a>
%F A286107 If A286105(A285735(n)) > A286105(A285734(n)), a(n) = A285735(n), otherwise a(n) = A285734(n), a(1) = 0.
%o A286107 (Scheme) (define (A286107 n) (cond ((= 1 n) 0) ((> (A286106 n) 0) (A285735 n)) (else (A285734 n))))
%o A286107 (Python)
%o A286107 from sympy.ntheory.factor_ import core
%o A286107 def issquarefree(n): return core(n) == n
%o A286107 def a285734(n):
%o A286107     if n==1: return 0
%o A286107     j=n//2
%o A286107     while True:
%o A286107         if issquarefree(j) and issquarefree(n - j): return j
%o A286107         else: j-=1
%o A286107 def a285735(n): return n - a285734(n)
%o A286107 def a286105(n): return 0 if n==1 else 1 + max(a286105(a285734(n)), a286105(a285735(n)))
%o A286107 def a286106(n): return 0 if n==1 else a286105(a285735(n)) - a286105(a285734(n))
%o A286107 def a286107(n): return 0 if n==1 else a285735(n) if a286106(n)>0 else a285734(n)
%o A286107 print([a286107(n) for n in range(1, 121)]) # _Indranil Ghosh_, May 02 2017
%Y A286107 Cf. A005117, A285734, A285735, A286104, A286105, A286106.
%K A286107 nonn
%O A286107 1,3
%A A286107 _Antti Karttunen_, May 02 2017