A286106 a(1) = 0, and for n > 1, a(n) = A286105(A285735(n)) - A286105(A285734(n)).

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, 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, 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

Offset

1,7

Links

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

Formula

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

Prog

(Scheme) (define (A286106 n) (if (= 1 n) 0 (- (A286105 (A285735 n)) (A286105 (A285734 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 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))
print([a286106(n) for n in range(1, 121)]) # Indranil Ghosh, May 02 2017

Crossrefs

Cf. A285734, A285735, A286105, A286107.

Sequence in context: A340671 A167687 A064692 * A079677 A286564 A316359

Adjacent sequences: A286103 A286104 A286105 * A286107 A286108 A286109

Keyword

sign

Author

Antti Karttunen, May 02 2017

Status

approved