A285709 a(n) = A000010(n) - A285699(n).

0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 2, 0, 0, 4, 0, 4, 0, 4, 0, 2, 0, 2, 0, 0, 0, 5, 0, 0, 14, 14, 14, 8, 0, 12, 12, 8, 0, 6, 0, 8, 6, 8, 0, 4, 0, 10, 8, 4, 0, 12, 10, 17, 6, 2, 0, 10, 0, 0, 22, 0, 8, 18, 0, 28, 2, 18, 0, 16, 0, 26, 10, 24, 32, 18, 0, 16, 0, 22, 0, 21, 4, 20, 50, 16, 0, 15, 30, 16, 48, 16, 2, 17, 0, 8, 42, 20, 0, 26, 0, 8, 24, 10, 0, 24, 0, 30, 42, 34, 0, 30, -2

Offset: 1

Author

Antti Karttunen, Apr 26 2017

Keywords

• sign
• look

Comments

The scatter plot has unusual "rays".

Links

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

Crossrefs

Cf. A000010, A007947, A051953, A079277, A285699, A285711.

Cf. A285710 (positions of zeros), A208815 (of negative terms).

Programs

Mathematica

Table[EulerPhi@ n - (n - If[n <= 2, n - 1, Module[{k = n - 2, e = Floor@ Log2@ n}, While[PowerMod[n, e, k] != 0, k--]; k]]), {n, 115}] (* Michael De Vlieger, Apr 26 2017 *)

PARI

A007947(n) = factorback(factorint(n)[, 1]); \\ From Andrew Lelechenko, May 09 2014
A079277(n) = { my(r); if((n > 1 && !bitand(n,(n-1))), (n/2), r=A007947(n); if(1==n,0,k = n-1; while(A007947(k*n) <> r, k = k-1); k)); };
A285709(n) = if(!n,n,(eulerphi(n)+A079277(n))-n);

Python

from sympy import divisors, totient
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 a285699(n): return 1 if n<2 else n - a079277(n)
def a(n): return totient(n) - a285699(n)
print([a(n) for n in range(1, 116)]) # Indranil Ghosh, Apr 26 2017

Scheme

(define (A285709 n) (- (A000010 n) (A285699 n)))

Formula

a(n) = A000010(n) - A285699(n).

For n > 1, a(n) = (A000010(n) + A079277(n)) - n = A079277(n) - A051953(n).