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

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

Offset: 1

Author

Antti Karttunen, May 02 2017

Keywords

• nonn

Comments

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

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

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 a286105(n): return 0 if n==1 else 1 + max(a286105(a285734(n)), a286105(a285735(n)))
def a286106(n): return 0 if n==1 else a286105(a285735(n)) - a286105(a285734(n))
def a286107(n): return 0 if n==1 else a285735(n) if a286106(n)>0 else a285734(n)
print([a286107(n) for n in range(1, 121)]) # Indranil Ghosh, May 02 2017

Scheme

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

Formula

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