A286106 - OEIS

%I #17 Apr 30 2021 06:05:55

%S 0,0,1,0,1,0,2,1,1,0,0,0,1,0,1,1,0,0,2,0,0,0,1,1,1,0,0,0,0,0,0,0,1,0,

%T 0,1,0,0,0,-1,-1,0,0,0,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,-1,

%U 0,0,0,0,0,1,0,1,0,-1,0,0,1,0,0,-1,0,0,0,0,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0

%N a(1) = 0, and for n > 1, a(n) = A286105(A285735(n)) - A286105(A285734(n)).

%H Antti Karttunen, <a href="/A286106/b286106.txt">Table of n, a(n) for n = 1..10000</a>

%F a(1) = 0, and for n > 1, a(n) = A286105(A285735(n)) - A286105(A285734(n)).

%o (Scheme) (define (A286106 n) (if (= 1 n) 0 (- (A286105 (A285735 n)) (A286105 (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=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 print([a286106(n) for n in range(1, 121)]) # _Indranil Ghosh_, May 02 2017

%Y Cf. A285734, A285735, A286105, A286107.

%K sign

%O 1,7

%A _Antti Karttunen_, May 02 2017