A285699 a(1) = 1; for n > 1, a(n) = n - A079277(n).

1, 1, 2, 2, 4, 2, 6, 4, 6, 2, 10, 3, 12, 6, 6, 8, 16, 2, 18, 4, 12, 6, 22, 6, 20, 10, 18, 12, 28, 3, 30, 16, 6, 2, 10, 4, 36, 6, 12, 8, 40, 6, 42, 12, 18, 14, 46, 12, 42, 10, 24, 20, 52, 6, 30, 7, 30, 26, 58, 6, 60, 30, 14, 32, 40, 2, 66, 4, 42, 6, 70, 8, 72, 10, 30, 12, 28, 6, 78, 16, 54, 18, 82, 3, 60, 22, 6, 24, 88, 9, 42, 28, 12, 30, 70, 15, 96, 34, 18, 20

Offset: 1

Author

Antti Karttunen, Apr 26 2017

Keywords

• nonn
• look

Comments

The scatter plot has unusual "rays".

Links

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

Crossrefs

Cf. A000010, A079277, A285710.

Programs

Mathematica

Table[n - If[n <= 2, n - 1, Module[{k = n - 2, e = Floor@ Log2@ n}, While[PowerMod[n, e, k] != 0, k--]; k]], {n, 100}] (* Michael De Vlieger, Apr 26 2017 *)

Python

from sympy import divisors
from sympy.ntheory.factor_ import core
def a007947(n): return max(i for i in divisors(n) if core(i) == i)
def a079277(n):
    k=n - 1
    while True:
        if a007947(k*n) == a007947(n): return k
        else: k-=1
def a(n): return 1 if n<2 else n - a079277(n)
print([a(n) for n in range(1, 101)]) # Indranil Ghosh, Apr 26 2017

Scheme

(define (A285699 n) (if (= 1 n) n (- n (A079277 n))))

Formula

a(1) = 1; for n > 1, a(n) = n - A079277(n).

Other identities. For all n >= 1:

a(A285710(n)) = A000010(A285710(n)). [A285710 gives all such matches.]