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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). 6

%I

%S 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 14,15,14,15,19,17,14,19,15,19,17,19,19,21,21,22,23,23,26,26,23,29,29,

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

%C After the initial zero, all terms are squarefree numbers (A005117).

%H Antti Karttunen, <a href="/A286107/b286107.txt">Table of n, a(n) for n = 1..10000</a>

%F If A286105(A285735(n)) > A286105(A285734(n)), a(n) = A285735(n), otherwise a(n) = A285734(n), a(1) = 0.

%o (Scheme) (define (A286107 n) (cond ((= 1 n) 0) ((> (A286106 n) 0) (A285735 n)) (else (A285734 n))))

%o (Python)

%o from sympy.ntheory.factor_ import core

%o def issquarefree(n): return core(n) == n

%o def a285734(n):

%o if n==1: return 0

%o j=int(n/2)

%o while True:

%o if issquarefree(j) and issquarefree(n - j): return j

%o else: j-=1

%o def a285735(n): return n - a285734(n)

%o def a286105(n): return 0 if n==1 else 1 + max(a286105(a285734(n)), a286105(a285735(n)))

%o def a286106(n): return 0 if n==1 else a286105(a285735(n)) - a286105(a285734(n))

%o def a286107(n): return 0 if n==1 else a285735(n) if a286106(n)>0 else a285734(n)

%o print [a286107(n) for n in xrange(1, 121)] # _Indranil Ghosh_, May 02 2017

%Y Cf. A005117, A285734, A285735, A286104, A286105, A286106.

%K nonn

%O 1,3

%A _Antti Karttunen_, May 02 2017

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Last modified May 24 06:53 EDT 2019. Contains 323529 sequences. (Running on oeis4.)