A285711 a(n) = gcd(A051953(n), A079277(n)), a(1) = 1.

1, 1, 1, 2, 1, 4, 1, 4, 3, 2, 1, 1, 1, 8, 1, 8, 1, 4, 1, 4, 9, 4, 1, 2, 5, 2, 9, 16, 1, 1, 1, 16, 1, 2, 1, 8, 1, 4, 3, 8, 1, 6, 1, 8, 3, 8, 1, 4, 7, 10, 1, 4, 1, 12, 5, 1, 3, 2, 1, 2, 1, 32, 1, 32, 1, 2, 1, 4, 1, 2, 1, 16, 1, 2, 5, 8, 1, 18, 1, 16, 27, 2, 1, 3, 1, 4, 1, 16, 1, 3, 1, 16, 3, 16, 1, 1, 1, 8, 3, 20, 1, 2, 1, 8, 3, 2, 1, 24, 1, 10, 3, 2, 1, 6, 1

Offset: 1

Author

Antti Karttunen, Apr 26 2017

Keywords

• nonn

Links

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

Crossrefs

Cf. A009195, A051953, A079277, A285707, A285709, A285710.

Programs

Mathematica

Table[GCD[n - EulerPhi@ n, If[n <= 2, 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 *)

Python

from sympy import divisors, totient, gcd
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==1 else gcd(n - totient(n), a079277(n))
print([a(n) for n in range(1, 151)]) # Indranil Ghosh, Apr 26 2017

Scheme

(define (A285711 n) (if (= 1 n) n (gcd (A051953 n) (A079277 n))))

Formula

a(1) = 1; for n > 1, a(n) = gcd(A051953(n), A079277(n)).