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A286104
If A286103(A285734(n)) < A286103(A285735(n)), a(n) = A285734(n), otherwise a(n) = A285735(n), a(1) = 0.
4
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, 15, 17, 17, 19, 17, 14, 19, 15, 19, 17, 19, 19, 21, 22, 22, 23, 23, 26, 26, 26, 29, 29, 26, 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
OFFSET
1,4
COMMENTS
After the initial zero, all terms are squarefree numbers (A005117).
LINKS
FORMULA
a(1) = 0, and for n > 1, if A286103(A285734(n)) < A286103(A285735(n)), a(n) = A285734(n), otherwise a(n) = A285735(n).
PROG
(Scheme) (define (A286104 n) (cond ((= 1 n) 0) ((< (A286103 (A285734 n)) (A286103 (A285735 n))) (A285734 n)) (else (A285735 n))))
(Python)
from sympy.ntheory.factor_ import core
def issquarefree(n): return core(n) == n
def a285734(n):
if n==1: return 0
j=n//2
while True:
if issquarefree(j) and issquarefree(n - j): return j
else: j-=1
def a285735(n): return n - a285734(n)
def a286103(n): return 0 if n==1 else 1 + min(a286103(a285734(n)), a286103(a285735(n)))
def a286104(n): return 0 if n==1 else a285734(n) if a286103(a285734(n)) < a286103(a285735(n)) else a285735(n)
print([a286104(n) for n in range(1, 121)]) # Indranil Ghosh, May 02 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, May 02 2017
STATUS
approved